\usepackage or this document’s own macros. Corpus-wide, \bm occurs 327 times, \Perp is defined by no package and spans 10 documents, and 11,088 of 11,624 undefined occurrences are the source document’s own macros. A row that looks wrong here may be correct, and one that looks right here may not compile. The LaTeX report renders through the document’s own preamble and is the surface to judge from.3720 rows
The page, the confidence and the picture of an inline formula are its HOST LINE's --- a formula has none of its own. A line's confidence is not a formula's.
| Identifier | Page | Conf. | LaTeX source | Rendered | Image |
|---|---|---|---|---|---|
| cardona-qft-methods_FO0001 | 8 | 1.000 | A d S / C F T | | |
| cardona-qft-methods_FO0002 | 8 | 1.000 | \mathcal{N}=4 | | |
| cardona-qft-methods_FO0003 | 74 | 1.000 | G | | |
| cardona-qft-methods_FO0004 | 14 | 1.000 | A | | |
| cardona-qft-methods_FO0005 | 14 | 0.992 | A=\int_{a \in \operatorname{Sp}(a)} a d P_{a} | | |
| cardona-qft-methods_FO0006 | 14 | 0.992 | \operatorname{Sp}(A) | | |
| cardona-qft-methods_FO0007 | 15 | 0.523 | \psi(\vec{x}) | | |
| cardona-qft-methods_FO0008 | 15 | 0.523 | \vec{x} \in \mathbb{R}^{4} | | |
| cardona-qft-methods_FO0009 | 15 | 0.523 | E | | |
| cardona-qft-methods_FO0010 | 15 | 0.523 | B \in | | |
| cardona-qft-methods_FO0011 | 15 | 0.803 | \operatorname{Function}\left(M=\mathbb{R}^{4}, \mathbb{R}^{3}\right) | | |
| cardona-qft-methods_FO0012 | 15 | 1.000 | x^{\mu} | | |
| cardona-qft-methods_FO0013 | 15 | 1.000 | g_{\mu \nu}(x) | | |
| cardona-qft-methods_FO0014 | 15 | 1.000 | e_{\mu}^{I}(x) | | |
| cardona-qft-methods_FO0015 | 15 | 1.000 | I | | |
| cardona-qft-methods_FO0016 | 15 | 1.000 | \phi | | |
| cardona-qft-methods_FO0017 | 15 | 1.000 | M | | |
| cardona-qft-methods_FO0018 | 15 | 1.000 | e_{\nu}^{\prime I}(x)=\frac{\partial x^{\mu}}{\partial \phi(x)^{\nu}} e_{\mu}^{I}(x) | | |
| cardona-qft-methods_FO0019 | 15 | 1.000 | \left(\square+m^{2}\right) \psi(\vec{x})=s_{b}(\vec{x}) | | |
| cardona-qft-methods_FO0020 | 15 | 1.000 | (i \not \partial- | | |
| cardona-qft-methods_FO0021 | 15 | 1.000 | m) \psi(\vec{x})=s_{f}(\vec{x}) | | |
| cardona-qft-methods_FO0022 | 15 | 1.000 | s_{b}, s_{f} | | |
| cardona-qft-methods_FO0023 | 15 | 1.000 | \not \partial | | |
| cardona-qft-methods_FO0024 | 15 | 0.999 | { }^{24,30} | | |
| cardona-qft-methods_FO0025 | 15 | 0.945 | (\mathcal{A}, \mathcal{H}, \mathcal{D}) | | |
| cardona-qft-methods_FO0026 | 15 | 0.945 | * | | |
| cardona-qft-methods_FO0027 | 15 | 0.945 | \mathcal{A} | | |
| cardona-qft-methods_FO0028 | 15 | 1.000 | \mathcal{H} | | |
| cardona-qft-methods_FO0029 | 15 | 1.000 | \psi | | |
| cardona-qft-methods_FO0030 | 15 | 1.000 | \mathcal{D} | | |
| cardona-qft-methods_FO0031 | 15 | 1.000 | \Lambda^{-1} | | |
| cardona-qft-methods_FO0032 | 16 | 1.000 | S(\mathcal{D}, \Lambda, f)=\operatorname{Tr}(f(\mathcal{D} / \Lambda)) | | |
| cardona-qft-methods_FO0033 | 16 | 1.000 | \Lambda \in \mathbb{R}^{+} | | |
| cardona-qft-methods_FO0034 | 16 | 1.000 | f | | |
| cardona-qft-methods_FO0035 | 16 | 1.000 | \Lambda \rightarrow \infty | | |
| cardona-qft-methods_FO0036 | 16 | 1.000 | M \times F | | |
| cardona-qft-methods_FO0037 | 16 | 1.000 | F | | |
| cardona-qft-methods_FO0038 | 16 | 1.000 | { }^{11,20,30} | | |
| cardona-qft-methods_FO0039 | 16 | 0.997 | \Psi | | |
| cardona-qft-methods_FO0040 | 16 | 1.000 | \mathcal{L}^{1, \infty}(\mathcal{H}) | | |
| cardona-qft-methods_FO0041 | 16 | 1.000 | \sum_{n=1}^{\infty} n^{-1} | | |
| cardona-qft-methods_FO0042 | 16 | 0.987 | (M, g) | | |
| cardona-qft-methods_FO0043 | 16 | 1.000 | E=\mathcal{C} \ell^{*} M | | |
| cardona-qft-methods_FO0044 | 16 | 1.000 | \mathcal{C} \ell T_{x}^{*} M | | |
| cardona-qft-methods_FO0045 | 16 | 1.000 | x \in M | | |
| cardona-qft-methods_FO0046 | 16 | 0.999 | \nabla^{S} | | |
| cardona-qft-methods_FO0047 | 16 | 0.999 | \not D=-i c \circ \nabla^{S} | | |
| cardona-qft-methods_FO0048 | 16 | 0.999 | c | | |
| cardona-qft-methods_FO0049 | 16 | 1.000 | g | | |
| cardona-qft-methods_FO0050 | 16 | 1.000 | e^{t \Delta}, t \in \mathbb{R}^{+} | | |
| cardona-qft-methods_FO0051 | 16 | 1.000 | t \rightarrow 0^{+} | | |
| cardona-qft-methods_FO0052 | 17 | 0.990 | \Delta | | |
| cardona-qft-methods_FO0053 | 17 | 1.000 | \mathcal{D}^{2} | | |
| cardona-qft-methods_FO0054 | 17 | 1.000 | \operatorname{Tr}(f(\mathcal{D} / \Lambda)) | | |
| cardona-qft-methods_FO0055 | 17 | 1.000 | \Lambda | | |
| cardona-qft-methods_FO0056 | 17 | 1.000 | |\mathcal{D}| | | |
| cardona-qft-methods_FO0057 | 17 | 1.000 | \mathbb{N}=\{1,2, \ldots\} | | |
| cardona-qft-methods_FO0058 | 17 | 1.000 | \mathbb{N}_{0}=\mathbb{N} \cup\{0\} | | |
| cardona-qft-methods_FO0059 | 17 | 1.000 | \mathbb{R}^{d} | | |
| cardona-qft-methods_FO0060 | 17 | 1.000 | d x=d x^{1} \wedge \cdots \wedge d x^{d} | | |
| cardona-qft-methods_FO0061 | 17 | 1.000 | \mathbb{S}^{d} | | |
| cardona-qft-methods_FO0062 | 17 | 1.000 | d | | |
| cardona-qft-methods_FO0063 | 17 | 1.000 | d \xi= | | |
| cardona-qft-methods_FO0064 | 17 | 1.000 | \left|\sum_{j=1}^{d}(-1)^{j-1} \xi_{j} d \xi_{1} \wedge \cdots \wedge \widehat{d \xi}_{j} \wedge \cdots \wedge d \xi_{d}\right| | | |
| cardona-qft-methods_FO0065 | 17 | 1.000 | \mathbb{S}^{d-1} | | |
| cardona-qft-methods_FO0066 | 17 | 1.000 | U, V | | |
| cardona-qft-methods_FO0067 | 17 | 0.998 | _{g} | | |
| cardona-qft-methods_FO0068 | 17 | 0.997 | \left\{\xi_{1}, \cdots, \xi_{d}\right\} | | |
| cardona-qft-methods_FO0069 | 17 | 0.997 | T_{x} M | | |
| cardona-qft-methods_FO0070 | 17 | 0.792 | d v o l_{g}\left(\xi_{1}, \cdots, \xi_{d}\right)=1 | | |
| cardona-qft-methods_FO0071 | 17 | 0.792 | \sqrt{\operatorname{det} g_{x}}|d x|=\left|d v o l_{g}\right| | | |
| cardona-qft-methods_FO0072 | 17 | 1.000 | \alpha \in \mathbb{N}^{d} | | |
| cardona-qft-methods_FO0073 | 17 | 1.000 | \partial_{x}^{\alpha}=\partial_{x_{1}}^{\alpha_{1}} \partial_{x_{2}}^{\alpha_{2}} \cdots \partial_{x_{d}}^{\alpha_{d}}, \quad|\alpha|=\sum_{i=1}^{d} \alpha_{i} | | |
| cardona-qft-methods_FO0074 | 17 | 1.000 | \alpha!=\alpha_{1} a_{2} \cdots \alpha_{d} | | |
| cardona-qft-methods_FO0075 | 17 | 1.000 | \xi \in \mathbb{R}^{d},|\xi|=\left(\sum_{k=1}^{d}\left|\xi_{k}\right|^{2}\right)^{1 / 2} | | |
| cardona-qft-methods_FO0076 | 17 | 1.000 | \mathcal{B}(\mathcal{H}), \mathcal{K}(\mathcal{H}), \mathcal{L}^{p}(\mathcal{H}) | | |
| cardona-qft-methods_FO0077 | 17 | 1.000 | p | | |
| cardona-qft-methods_FO0078 | 17 | 1.000 | \mathcal{L}^{1}(\mathcal{H}) | | |
| cardona-qft-methods_FO0079 | 17 | 0.998 | \Psi D O(M) | | |
| cardona-qft-methods_FO0080 | 17 | 1.000 | { }^{99,102} | | |
| cardona-qft-methods_FO0081 | 17 | 1.000 | { }^{86,87} | | |
| cardona-qft-methods_FO0082 | 17 | 1.000 | { }^{3,33} | | |
| cardona-qft-methods_FO0083 | 17 | 1.000 | { }^{49,82,83,104,105} | | |
| cardona-qft-methods_FO0084 | 18 | 1.000 | m \in \mathbb{C} | | |
| cardona-qft-methods_FO0085 | 18 | 1.000 | \sigma(x, \xi) | | |
| cardona-qft-methods_FO0086 | 18 | 1.000 | m | | |
| cardona-qft-methods_FO0087 | 18 | 1.000 | C^{\infty} | | |
| cardona-qft-methods_FO0088 | 18 | 1.000 | (x, \xi) \in U \times \mathbb{R}^{d} \rightarrow \mathbb{C} | | |
| cardona-qft-methods_FO0089 | 18 | 0.915 | \left|\partial_{x}^{\alpha} \partial_{\xi}^{\beta} \sigma(x, \xi)\right| \leq C_{\alpha \beta}(x)(1+|\xi|)^{\Re(m)-|\beta|}, C_{\alpha \beta} | | |
| cardona-qft-methods_FO0090 | 18 | 0.915 | U | | |
| cardona-qft-methods_FO0091 | 18 | 1.000 | \sigma(x, \xi) \simeq \sum_{j \geq 0} \sigma_{m-j}(x, \xi) | | |
| cardona-qft-methods_FO0092 | 18 | 1.000 | \sigma_{k} | | |
| cardona-qft-methods_FO0093 | 18 | 1.000 | k | | |
| cardona-qft-methods_FO0094 | 18 | 1.000 | \xi | | |
| cardona-qft-methods_FO0095 | 18 | 1.000 | \simeq | | |
| cardona-qft-methods_FO0096 | 18 | 1.000 | |\xi| \geq 1 | | |
| cardona-qft-methods_FO0097 | 18 | 1.000 | C_{N \alpha \beta} | | |
| cardona-qft-methods_FO0098 | 18 | 1.000 | S^{m}\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0099 | 18 | 1.000 | a \in C^{\infty}\left(U \times U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0100 | 18 | 1.000 | K \subset U | | |
| cardona-qft-methods_FO0101 | 18 | 1.000 | \alpha, \beta, \gamma \in \mathbb{N}^{d} | | |
| cardona-qft-methods_FO0102 | 18 | 1.000 | C_{K \alpha \beta \gamma} | | |
| cardona-qft-methods_FO0103 | 18 | 1.000 | A^{m}(U) | | |
| cardona-qft-methods_FO0104 | 18 | 1.000 | \sigma \in S^{m}\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0105 | 18 | 1.000 | \sigma(\cdot, D): u \in C_{c}^{\infty}(U) \rightarrow | | |
| cardona-qft-methods_FO0106 | 18 | 1.000 | C^{\infty}(U) | | |
| cardona-qft-methods_FO0107 | 18 | 0.994 | \sigma(\cdot, D) | | |
| cardona-qft-methods_FO0108 | 18 | 0.848 | O p(\sigma) | | |
| cardona-qft-methods_FO0109 | 18 | 0.848 | \sigma(x, \xi)=\sum_{\alpha} a_{\alpha}(x) \xi^{\alpha} | | |
| cardona-qft-methods_FO0110 | 18 | 0.848 | \sigma(x, D)= | | |
| cardona-qft-methods_FO0111 | 18 | 1.000 | \sum_{\alpha} a_{\alpha}(x) D_{x}^{\alpha} | | |
| cardona-qft-methods_FO0112 | 18 | 1.000 | D_{x}=-i \partial_{x} | | |
| cardona-qft-methods_FO0113 | 18 | 1.000 | \mathcal{D}_{c}^{\prime}(U) | | |
| cardona-qft-methods_FO0114 | 18 | 0.999 | \mathcal{D}^{\prime}(U) | | |
| cardona-qft-methods_FO0115 | 18 | 1.000 | |\alpha|=m | | |
| cardona-qft-methods_FO0116 | 18 | 1.000 | \sigma(x, D) | | |
| cardona-qft-methods_FO0117 | 18 | 0.907 | \operatorname{Op}(a) | | |
| cardona-qft-methods_FO0118 | 18 | 0.907 | a | | |
| cardona-qft-methods_FO0119 | 18 | 0.997 | P: C_{c}^{\infty}(U) \rightarrow C^{\infty}(U) | | |
| cardona-qft-methods_FO0120 | 18 | 1.000 | C^{\infty}(U \times U) | | |
| cardona-qft-methods_FO0121 | 18 | 1.000 | \Psi D O^{-\infty}(U) | | |
| cardona-qft-methods_FO0122 | 19 | 1.000 | \Psi D O^{m}(U) | | |
| cardona-qft-methods_FO0123 | 19 | 1.000 | P | | |
| cardona-qft-methods_FO0124 | 19 | 1.000 | P: C_{c}^{\infty}(U) \rightarrow C^{\infty}(U), P u(x)=(\sigma(x, D)+ | | |
| cardona-qft-methods_FO0125 | 19 | 0.914 | R)(u) | | |
| cardona-qft-methods_FO0126 | 19 | 0.914 | \sigma \in S^{m}\left(U \times \mathbb{R}^{d}\right), R \in \Psi D O^{-\infty} | | |
| cardona-qft-methods_FO0127 | 19 | 0.914 | \sigma | | |
| cardona-qft-methods_FO0128 | 19 | 0.861 | m \in \mathbb{R} | | |
| cardona-qft-methods_FO0129 | 19 | 0.861 | (2), a(x, y, \xi)= | | |
| cardona-qft-methods_FO0130 | 19 | 1.000 | e^{-i(x-y) \cdot \xi} k(x, y) \phi(\xi) | | |
| cardona-qft-methods_FO0131 | 19 | 1.000 | \phi \in C_{c}^{\infty}\left(\mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0132 | 19 | 1.000 | \int_{\mathbb{R}^{d}} \phi(\xi) d \xi= | | |
| cardona-qft-methods_FO0133 | 19 | 1.000 | (2 \pi)^{d} | | |
| cardona-qft-methods_FO0134 | 19 | 1.000 | k^{\sigma(x, D)} | | |
| cardona-qft-methods_FO0135 | 19 | 1.000 | \sigma^{A}(x, \xi)=e^{-i x \cdot \xi} A\left(x \rightarrow e^{i x \cdot \xi}\right) | | |
| cardona-qft-methods_FO0136 | 19 | 1.000 | k^{A}(x, y, \xi) | | |
| cardona-qft-methods_FO0137 | 19 | 1.000 | k_{\sigma}^{A}(x, y) | | |
| cardona-qft-methods_FO0138 | 19 | 1.000 | \sigma^{A}(x, \xi)= | | |
| cardona-qft-methods_FO0139 | 19 | 1.000 | e^{i D_{\xi} D_{y}} k^{A}(x, y, \xi)_{\mid y=x} | | |
| cardona-qft-methods_FO0140 | 19 | 1.000 | e^{i D_{\xi} D_{y}}=1+i D_{\xi} D_{y}-\frac{1}{2}\left(D_{\xi} D_{y}\right)^{2}+\cdots | | |
| cardona-qft-methods_FO0141 | 19 | 1.000 | A=O p\left(\sigma^{A}\right)+R | | |
| cardona-qft-methods_FO0142 | 19 | 1.000 | R | | |
| cardona-qft-methods_FO0143 | 19 | 1.000 | P_{1} \in \Psi D O^{m_{1}} | | |
| cardona-qft-methods_FO0144 | 19 | 1.000 | P_{2} \in \Psi D O^{m_{2}} | | |
| cardona-qft-methods_FO0145 | 19 | 1.000 | P_{1} P_{2} \in | | |
| cardona-qft-methods_FO0146 | 19 | 1.000 | \Psi D O^{m_{1}+m_{2}} | | |
| cardona-qft-methods_FO0147 | 19 | 1.000 | P_{1} P_{2} | | |
| cardona-qft-methods_FO0148 | 19 | 1.000 | \sigma_{m_{1}+m_{2}}^{P_{1} P_{2}}(x, \xi)=\sigma_{m_{1}}^{P_{1}}(x, \xi) \sigma_{m_{2}}^{P_{2}}(x, \xi) | | |
| cardona-qft-methods_FO0149 | 19 | 1.000 | P \in \Psi D O^{m}(U) | | |
| cardona-qft-methods_FO0150 | 19 | 1.000 | \phi \in \operatorname{Diff}(U, V) | | |
| cardona-qft-methods_FO0151 | 19 | 1.000 | V | | |
| cardona-qft-methods_FO0152 | 19 | 1.000 | \phi_{*} P: f \in C^{\infty}(V) \rightarrow P(f \circ \phi) \circ \phi^{-1} | | |
| cardona-qft-methods_FO0153 | 19 | 1.000 | \phi_{*} P \in \Psi D O^{m}(V) | | |
| cardona-qft-methods_FO0154 | 20 | 1.000 | \phi_{\alpha} | | |
| cardona-qft-methods_FO0155 | 20 | 1.000 | \alpha | | |
| cardona-qft-methods_FO0156 | 20 | 1.000 | \sigma^{\phi_{*} P}{ }_{m}=\phi_{*} \sigma_{m}^{P} | | |
| cardona-qft-methods_FO0157 | 20 | 1.000 | \sigma^{P}(x, \xi)=e^{-i x \cdot \xi} P\left(x \rightarrow e^{i x \cdot \xi}\right) | | |
| cardona-qft-methods_FO0158 | 20 | 1.000 | \xi \rightarrow t \xi | | |
| cardona-qft-methods_FO0159 | 20 | 1.000 | t>0 | | |
| cardona-qft-methods_FO0160 | 20 | 1.000 | t^{-m} e^{-i t x \cdot \xi} P e^{i t x \cdot \xi}=t^{-m} \sigma^{P}(x, t \xi) \simeq | | |
| cardona-qft-methods_FO0161 | 20 | 1.000 | t^{-m} \sum_{j \geq 0} \sigma_{m-j}^{P}(x, t \xi)=\sigma_{m}^{P}(x, \xi)+o\left(t^{-1}\right) | | |
| cardona-qft-methods_FO0162 | 20 | 1.000 | m \geq 0 | | |
| cardona-qft-methods_FO0163 | 20 | 1.000 | h \in C^{\infty}(U) | | |
| cardona-qft-methods_FO0164 | 20 | 1.000 | d h(x)=\xi | | |
| cardona-qft-methods_FO0165 | 20 | 1.000 | \Psi D O^{m}(M) | | |
| cardona-qft-methods_FO0166 | 20 | 1.000 | C_{c}^{\infty}(M) \rightarrow C^{\infty}(M) | | |
| cardona-qft-methods_FO0167 | 20 | 1.000 | k^{P} \in C^{\infty}(M \times M) | | |
| cardona-qft-methods_FO0168 | 20 | 1.000 | f \in C_{c}^{\infty}(\phi(U)) \rightarrow P(f \circ \phi) \circ \phi^{-1} \in C^{\infty}(\phi(U)) | | |
| cardona-qft-methods_FO0169 | 20 | 0.999 | \Psi D O^{m}(\phi(U)) | | |
| cardona-qft-methods_FO0170 | 20 | 0.999 | \left(U, \phi: U \rightarrow \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0171 | 20 | 1.000 | P: \Gamma_{c}^{\infty}(M, E) \rightarrow \Gamma^{\infty}(M, E) | | |
| cardona-qft-methods_FO0172 | 20 | 1.000 | \Psi D O^{m}(M, E) | | |
| cardona-qft-methods_FO0173 | 20 | 1.000 | k^{P} | | |
| cardona-qft-methods_FO0174 | 20 | 1.000 | \Psi D O | | |
| cardona-qft-methods_FO0175 | 20 | 1.000 | \sigma_{m}^{P} | | |
| cardona-qft-methods_FO0176 | 20 | 1.000 | T^{*} M \rightarrow M | | |
| cardona-qft-methods_FO0177 | 20 | 1.000 | P \in \Psi D O^{m} | | |
| cardona-qft-methods_FO0178 | 20 | 1.000 | P \in \Psi D O^{m}(M, E) | | |
| cardona-qft-methods_FO0179 | 20 | 1.000 | \sigma_{m}^{P}(x, \xi) | | |
| cardona-qft-methods_FO0180 | 20 | 1.000 | 0 \neq \xi \in T M_{x}^{*} | | |
| cardona-qft-methods_FO0181 | 21 | 1.000 | \left|\sigma^{P}(x, \xi)\right| \geq c_{1}(x)|\xi|^{m} | | |
| cardona-qft-methods_FO0182 | 21 | 1.000 | |\xi| \geq c_{2}(x), x \in U | | |
| cardona-qft-methods_FO0183 | 21 | 1.000 | c_{1}, c_{2} | | |
| cardona-qft-methods_FO0184 | 21 | 0.967 | O p(\sigma) \in \Psi D O^{m}(U) | | |
| cardona-qft-methods_FO0185 | 21 | 1.000 | \sigma^{\prime} \in S^{-m}\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0186 | 21 | 1.000 | \sigma \circ \sigma^{\prime}=1 | | |
| cardona-qft-methods_FO0187 | 21 | 1.000 | \sigma^{\prime} \circ \sigma=1 | | |
| cardona-qft-methods_FO0188 | 21 | 0.998 | \operatorname{Op}(\sigma) \operatorname{Op}\left(\sigma^{\prime}\right)=\operatorname{Op}\left(\sigma^{\prime}\right) \operatorname{Op}(\sigma)=1 | | |
| cardona-qft-methods_FO0189 | 21 | 1.000 | O p\left(\sigma^{\prime}\right) \in \Psi D O^{-m}(U) | | |
| cardona-qft-methods_FO0190 | 21 | 1.000 | P \in \Psi D O(M, E) | | |
| cardona-qft-methods_FO0191 | 21 | 1.000 | L^{2}(M, E) | | |
| cardona-qft-methods_FO0192 | 21 | 1.000 | \Re(m) \leq 0 | | |
| cardona-qft-methods_FO0193 | 21 | 1.000 | P \in \Psi D O^{-m}(M, E) | | |
| cardona-qft-methods_FO0194 | 21 | 1.000 | \Re(m)> | | |
| cardona-qft-methods_FO0195 | 21 | 1.000 | r | | |
| cardona-qft-methods_FO0196 | 21 | 1.000 | s \in \Gamma^{\infty}(M, E), t^{*} \in \Gamma^{\infty}\left(M, E^{*}\right) | | |
| cardona-qft-methods_FO0197 | 21 | 1.000 | f \in C^{\infty}(M) \rightarrow | | |
| cardona-qft-methods_FO0198 | 21 | 1.000 | \left\langle t^{*}, P(f s)\right\rangle \in C^{\infty}(M) | | |
| cardona-qft-methods_FO0199 | 21 | 1.000 | (U, \phi) | | |
| cardona-qft-methods_FO0200 | 21 | 1.000 | r \times r | | |
| cardona-qft-methods_FO0201 | 21 | 1.000 | -m | | |
| cardona-qft-methods_FO0202 | 21 | 1.000 | C^{\infty}\left(T^{*} U\right) \otimes \operatorname{End}(E) | | |
| cardona-qft-methods_FO0203 | 21 | 1.000 | \operatorname{End}(E) \simeq | | |
| cardona-qft-methods_FO0204 | 21 | 1.000 | M_{r}(\mathbb{C}) | | |
| cardona-qft-methods_FO0205 | 21 | 1.000 | \sigma_{-m}^{P}(x, \xi): E_{x} \rightarrow | | |
| cardona-qft-methods_FO0206 | 21 | 1.000 | E_{x} | | |
| cardona-qft-methods_FO0207 | 21 | 1.000 | \xi \in T_{x}^{*} M | | |
| cardona-qft-methods_FO0208 | 21 | 1.000 | T^{*} M | | |
| cardona-qft-methods_FO0209 | 21 | 1.000 | h \in C^{\infty}(M) | | |
| cardona-qft-methods_FO0210 | 21 | 1.000 | d_{x} h=\xi | | |
| cardona-qft-methods_FO0211 | 21 | 1.000 | \mathbb{R}^{d} \backslash\{0\} | | |
| cardona-qft-methods_FO0212 | 21 | 1.000 | \mathcal{S} | | |
| cardona-qft-methods_FO0213 | 21 | 1.000 | \mathcal{S}^{\prime} | | |
| cardona-qft-methods_FO0214 | 21 | 1.000 | f_{\lambda}(\xi)=f(\lambda \xi), \lambda \in \mathbb{R}_{+}^{*} | | |
| cardona-qft-methods_FO0215 | 21 | 1.000 | \tau \in \mathcal{S}^{\prime} \rightarrow \tau_{\lambda} | | |
| cardona-qft-methods_FO0216 | 21 | 0.974 | \left\langle\tau_{\lambda}, f\right\rangle=\lambda^{-d}\left\langle\tau, f_{\lambda^{-1}}\right\rangle | | |
| cardona-qft-methods_FO0217 | 21 | 0.974 | f \in \mathcal{S} | | |
| cardona-qft-methods_FO0218 | 21 | 0.974 | \tau \in \mathcal{S}^{\prime} | | |
| cardona-qft-methods_FO0219 | 21 | 1.000 | \tau_{\lambda}=\lambda^{m} \tau | | |
| cardona-qft-methods_FO0220 | 22 | 1.000 | \sigma \in C^{\infty}\left(\mathbb{R}^{d} \backslash\{0\}\right) | | |
| cardona-qft-methods_FO0221 | 22 | 1.000 | k \in \mathbb{Z} | | |
| cardona-qft-methods_FO0222 | 22 | 1.000 | k>-d | | |
| cardona-qft-methods_FO0223 | 22 | 1.000 | k=-d | | |
| cardona-qft-methods_FO0224 | 22 | 1.000 | c_{\sigma}=\int_{\mathbb{S}^{d-1}} \sigma(\xi) d \xi | | |
| cardona-qft-methods_FO0225 | 22 | 1.000 | \tau_{\lambda}=\lambda^{-d}\left(\tau+c_{\sigma} \log (\lambda) \delta_{0}\right) | | |
| cardona-qft-methods_FO0226 | 22 | 0.807 | \operatorname{kernel} k^{P} | | |
| cardona-qft-methods_FO0227 | 22 | 0.807 | P \in \Psi D O | | |
| cardona-qft-methods_FO0228 | 22 | 0.954 | \tau=\phi \circ \tau+(1-\phi) \circ \tau | | |
| cardona-qft-methods_FO0229 | 22 | 0.954 | \phi=1 | | |
| cardona-qft-methods_FO0230 | 22 | 1.000 | \tau | | |
| cardona-qft-methods_FO0231 | 22 | 0.919 | \phi \circ \tau | | |
| cardona-qft-methods_FO0232 | 22 | 0.919 | (\phi \circ \tau)^{\vee} \in \mathcal{S}^{\prime} | | |
| cardona-qft-methods_FO0233 | 22 | 0.529 | \tau^{\vee} | | |
| cardona-qft-methods_FO0234 | 22 | 0.529 | ((1-\phi) \circ \tau)^{\vee} | | |
| cardona-qft-methods_FO0235 | 22 | 0.979 | P \in \Psi D O^{m}(U), m \in \mathbb{Z} | | |
| cardona-qft-methods_FO0236 | 22 | 1.000 | a_{j}(x, y) \in C^{\infty}(U \times U \backslash\{x\}) | | |
| cardona-qft-methods_FO0237 | 22 | 1.000 | j | | |
| cardona-qft-methods_FO0238 | 22 | 1.000 | y | | |
| cardona-qft-methods_FO0239 | 22 | 1.000 | c_{P}(x) \in C^{\infty}(U) | | |
| cardona-qft-methods_FO0240 | 22 | 1.000 | P \in \Psi D O^{m}(M, E), m \in \mathbb{Z} | | |
| cardona-qft-methods_FO0241 | 22 | 1.000 | a_{j} | | |
| cardona-qft-methods_FO0242 | 22 | 1.000 | y, c_{P} | | |
| cardona-qft-methods_FO0243 | 22 | 0.990 | c_{P}(x)|d x| | | |
| cardona-qft-methods_FO0244 | 22 | 1.000 | c_{P} | | |
| cardona-qft-methods_FO0245 | 23 | 1.000 | \int_{M} c_{P}(x)|d x| | | |
| cardona-qft-methods_FO0246 | 23 | 1.000 | \mathbb{C} | | |
| cardona-qft-methods_FO0247 | 23 | 1.000 | m \in \mathbb{C} \backslash \mathbb{Z} | | |
| cardona-qft-methods_FO0248 | 23 | 1.000 | \Omega | | |
| cardona-qft-methods_FO0249 | 23 | 1.000 | \sigma: \Omega \rightarrow S^{m}\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0250 | 23 | 1.000 | z \in \Omega \rightarrow \sigma(z)(x, \xi) | | |
| cardona-qft-methods_FO0251 | 23 | 1.000 | x \in U, \xi \in \mathbb{R}^{d} | | |
| cardona-qft-methods_FO0252 | 23 | 1.000 | m(z) | | |
| cardona-qft-methods_FO0253 | 23 | 1.000 | \sigma(z) | | |
| cardona-qft-methods_FO0254 | 23 | 1.000 | \sigma(z) \simeq \sum_{j} \sigma_{m(z)-j}(z) | | |
| cardona-qft-methods_FO0255 | 23 | 1.000 | z | | |
| cardona-qft-methods_FO0256 | 23 | 1.000 | z \rightarrow \sigma_{m(z)-j}(z) | | |
| cardona-qft-methods_FO0257 | 23 | 1.000 | C^{\infty}\left(U \times \mathbb{R}^{d} \backslash\{0\}\right) | | |
| cardona-qft-methods_FO0258 | 23 | 1.000 | \partial_{z} \sigma(z)(x, \xi) | | |
| cardona-qft-methods_FO0259 | 23 | 1.000 | U \times \mathbb{R}^{d} | | |
| cardona-qft-methods_FO0260 | 23 | 1.000 | \partial_{z} \sigma(z)(x, \xi) \simeq \sum_{j \geq 0} \partial_{z} \sigma_{m(z)-j}(z)(x, \xi) | | |
| cardona-qft-methods_FO0261 | 23 | 1.000 | P: \Omega \subset \mathbb{C} \rightarrow \Psi D O(U) | | |
| cardona-qft-methods_FO0262 | 23 | 1.000 | P(z)=\sigma(z)(\cdot, D)+R(z) | | |
| cardona-qft-methods_FO0263 | 23 | 1.000 | \sigma: \Omega \rightarrow S\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0264 | 23 | 1.000 | R: \Omega \rightarrow C^{\infty}(U \times U) | | |
| cardona-qft-methods_FO0265 | 23 | 1.000 | \Psi D O(M, E) | | |
| cardona-qft-methods_FO0266 | 23 | 1.000 | P \in \Psi D O^{m}(U), m \in \mathbb{C} | | |
| cardona-qft-methods_FO0267 | 23 | 1.000 | Q \in \Psi D O^{m}(M, E) | | |
| cardona-qft-methods_FO0268 | 23 | 1.000 | \Re(m)>0 | | |
| cardona-qft-methods_FO0269 | 23 | 0.994 | Q | | |
| cardona-qft-methods_FO0270 | 23 | 0.994 | \operatorname{Spectrum}(Q) \cap | | |
| cardona-qft-methods_FO0271 | 23 | 1.000 | \mathbb{R}^{-}=\emptyset | | |
| cardona-qft-methods_FO0272 | 23 | 1.000 | \Gamma | | |
| cardona-qft-methods_FO0273 | 23 | 1.000 | \lambda^{z} | | |
| cardona-qft-methods_FO0274 | 23 | 1.000 | z=0 | | |
| cardona-qft-methods_FO0275 | 24 | 1.000 | \Re(s)<0, Q^{s}=\frac{1}{i 2 \pi} \int_{\Gamma} \lambda^{s}(\lambda-Q)^{-1} d \lambda | | |
| cardona-qft-methods_FO0276 | 24 | 1.000 | s \rightarrow Q^{s} | | |
| cardona-qft-methods_FO0277 | 24 | 1.000 | Q^{0} | | |
| cardona-qft-methods_FO0278 | 24 | 1.000 | Q^{1} | | |
| cardona-qft-methods_FO0279 | 24 | 1.000 | \Re(s) \leq 0 | | |
| cardona-qft-methods_FO0280 | 24 | 0.997 | S_{\text {int }} | | |
| cardona-qft-methods_FO0281 | 24 | 1.000 | L: \sigma \in S_{\text {int }}^{\mathbb{Z}}\left(\mathbb{R}^{d}\right) \rightarrow L(\sigma)=\check{\sigma}(0)=\frac{1}{(2 \pi)^{d}} \int_{\mathbb{R}^{d}} \sigma(\xi) d \xi | | |
| cardona-qft-methods_FO0282 | 24 | 0.223 | L | | |
| cardona-qft-methods_FO0283 | 24 | 0.223 | \widetilde{L} | | |
| cardona-qft-methods_FO0284 | 24 | 0.223 | \left.S^{\mathbb{C}} \mathbb{Z}^{( } \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0285 | 24 | 0.748 | \sigma(\xi) \simeq \sum_{j} \sigma_{m-j}(\xi), m \in \mathbb{C} \backslash \mathbb{Z}, \widetilde{L}(\sigma)=\left(\sigma-\sum_{j \leq N} \tau_{m-j}\right)^{\sim}(0)= | | |
| cardona-qft-methods_FO0286 | 24 | 1.000 | \frac{1}{(2 \pi)^{d}} \int_{\mathbb{R}^{d}}\left(\sigma-\sum_{j \leq N} \tau_{m-j}\right)(\xi) d \xi | | |
| cardona-qft-methods_FO0287 | 24 | 1.000 | \sigma, N | | |
| cardona-qft-methods_FO0288 | 24 | 1.000 | N>\Re(m)+d | | |
| cardona-qft-methods_FO0289 | 24 | 1.000 | \tau_{m-j} | | |
| cardona-qft-methods_FO0290 | 24 | 1.000 | \sigma_{m-j} | | |
| cardona-qft-methods_FO0291 | 24 | 0.976 | \sigma: \mathbb{C} \rightarrow S\left(\mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0292 | 24 | 0.976 | (\sigma(s))=s | | |
| cardona-qft-methods_FO0293 | 24 | 1.000 | \widetilde{L}(\sigma(s)) | | |
| cardona-qft-methods_FO0294 | 24 | 1.000 | \mathbb{Z} | | |
| cardona-qft-methods_FO0295 | 24 | 1.000 | p \in \mathbb{Z} | | |
| cardona-qft-methods_FO0296 | 24 | 0.997 | \operatorname{Res}_{s=p} \widetilde{L}(\sigma(s))=-\frac{1}{(2 \pi)^{d}} \int_{\mathbb{S}^{d-1}} \sigma_{-d}(p)(\xi) d \xi | | |
| cardona-qft-methods_FO0297 | 24 | 1.000 | { }^{109,110} | | |
| cardona-qft-methods_FO0298 | 24 | 1.000 | \mathcal{D} \in \Psi D O(M, E) | | |
| cardona-qft-methods_FO0299 | 24 | 0.935 | \Psi D O_{\text {int }}(M, E)=\left\{Q \in \Psi D O^{\mathbb{C}}(M, E) \mid \Re(\operatorname{order}(Q))<-d\right\} | | |
| cardona-qft-methods_FO0300 | 24 | 1.000 | P \in \Psi D O_{\text {int }}(M, E) | | |
| cardona-qft-methods_FO0301 | 24 | 1.000 | k^{P}(x, x) | | |
| cardona-qft-methods_FO0302 | 24 | 1.000 | M \times M | | |
| cardona-qft-methods_FO0303 | 24 | 1.000 | \operatorname{End}(E) | | |
| cardona-qft-methods_FO0304 | 24 | 1.000 | P \in \Psi D O^{\mathbb{Z}}(M, E) | | |
| cardona-qft-methods_FO0305 | 24 | 1.000 | P \in \Psi D O_{\text {int }}(M, E) \rightarrow \operatorname{Tr}(P) \in \mathbb{C} | | |
| cardona-qft-methods_FO0306 | 24 | 1.000 | \Psi D O^{\mathbb{C} \backslash \mathbb{Z}}(M, E) | | |
| cardona-qft-methods_FO0307 | 24 | 1.000 | s \in \mathbb{C} \rightarrow \operatorname{Tr}\left(P|\mathcal{D}|^{-s}\right) | | |
| cardona-qft-methods_FO0308 | 25 | 1.000 | c_{P}(x)= | | |
| cardona-qft-methods_FO0309 | 25 | 1.000 | \frac{1}{(2 \pi)^{d}} \int_{\mathbb{S}^{d-1}} \operatorname{tr}\left(\sigma_{-d}^{P}(x, \xi)\right) d \xi | | |
| cardona-qft-methods_FO0310 | 25 | 1.000 | \Psi D O^{\mathbb{Z}}(M, E) | | |
| cardona-qft-methods_FO0311 | 25 | 1.000 | s \rightarrow \operatorname{Tr}\left(P|\mathcal{D}|^{-s}\right) | | |
| cardona-qft-methods_FO0312 | 25 | 1.000 | P \in \Psi D O^{\mathbb{C} \backslash \mathbb{Z}}(M, E) | | |
| cardona-qft-methods_FO0313 | 25 | 1.000 | \Psi D O_{\text {int }}(M, E) | | |
| cardona-qft-methods_FO0314 | 25 | 1.000 | s=0 | | |
| cardona-qft-methods_FO0315 | 25 | 1.000 | L_{\phi}(\sigma)= | | |
| cardona-qft-methods_FO0316 | 25 | 0.999 | \operatorname{Tr}(\phi \sigma(x, D)) | | |
| cardona-qft-methods_FO0317 | 25 | 0.999 | \sigma \in S_{\text {int }}\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0318 | 25 | 0.999 | \phi \in C^{\infty}(U) | | |
| cardona-qft-methods_FO0319 | 25 | 1.000 | P=\sigma(\cdot, D) | | |
| cardona-qft-methods_FO0320 | 25 | 0.999 | L_{\phi} | | |
| cardona-qft-methods_FO0321 | 25 | 0.999 | S^{\mathbb{C} \backslash \mathbb{Z}}\left(U \times \mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0322 | 25 | 0.999 | \widetilde{L}_{\phi}(\sigma)= | | |
| cardona-qft-methods_FO0323 | 25 | 0.998 | \int_{U} \phi(x) \widetilde{L}_{\phi}(\sigma(x, \cdot))|d x| | | |
| cardona-qft-methods_FO0324 | 25 | 1.000 | \sigma(x, \xi)=\sigma(s)(x, \xi) | | |
| cardona-qft-methods_FO0325 | 25 | 1.000 | s | | |
| cardona-qft-methods_FO0326 | 25 | 1.000 | x | | |
| cardona-qft-methods_FO0327 | 25 | 1.000 | \widetilde{L}_{\phi}(\sigma(s)(x, \cdot)) | | |
| cardona-qft-methods_FO0328 | 25 | 1.000 | \widetilde{L}_{\phi}(\sigma(s)) | | |
| cardona-qft-methods_FO0329 | 25 | 1.000 | \mathbb{C} \backslash \mathbb{Z} | | |
| cardona-qft-methods_FO0330 | 25 | 1.000 | \operatorname{order}(\sigma(s))=s | | |
| cardona-qft-methods_FO0331 | 25 | 1.000 | p \in \mathbb{Z}, \operatorname{Res}_{s=p} \widetilde{L}_{\phi}(\sigma(s))=-\frac{1}{(2 \pi)^{d}} \int_{U} \int_{\mathbb{S}^{d-1}} \phi(x) \sigma_{-d}(p)(x, \xi) d \xi|d x|= | | |
| cardona-qft-methods_FO0332 | 25 | 1.000 | \int_{U} \phi(x) c_{P p}(x)|d x| | | |
| cardona-qft-methods_FO0333 | 25 | 1.000 | P=O p\left(\sigma_{p}(x, \xi)\right) | | |
| cardona-qft-methods_FO0334 | 25 | 1.000 | \operatorname{Tr} | | |
| cardona-qft-methods_FO0335 | 25 | 1.000 | P: \mathbb{C} \rightarrow \Psi D O^{\mathbb{Z}}(M, E) | | |
| cardona-qft-methods_FO0336 | 25 | 1.000 | \operatorname{order}(P(s))= | | |
| cardona-qft-methods_FO0337 | 25 | 0.814 | \operatorname{Tr}(P(s)) | | |
| cardona-qft-methods_FO0338 | 25 | 0.814 | \operatorname{Res}_{s=p}^{\operatorname{Tr}}(P(s))= | | |
| cardona-qft-methods_FO0339 | 25 | 0.987 | -\int_{M} c_{P(p)}(x)|d x| | | |
| cardona-qft-methods_FO0340 | 25 | 0.987 | P(s)= | | |
| cardona-qft-methods_FO0341 | 25 | 1.000 | P|\mathcal{D}|^{-s} | | |
| cardona-qft-methods_FO0342 | 25 | 0.997 | P_{1}, P_{2} \in \Psi D O^{\mathbb{Z}}(M, E) | | |
| cardona-qft-methods_FO0343 | 25 | 0.956 | (i), \operatorname{Tr}\left(P_{1} P_{2}|\mathcal{D}|^{-s}\right)=\operatorname{Tr}\left(P_{2}|\mathcal{D}|^{-s} P_{1}\right) | | |
| cardona-qft-methods_FO0344 | 25 | 1.000 | P(s) | | |
| cardona-qft-methods_FO0346 | 26 | 0.852 | \Psi D O^{-m}(M, E), m \in \mathbb{N} | | |
| cardona-qft-methods_FO0347 | 26 | 1.000 | d \geq 2 | | |
| cardona-qft-methods_FO0348 | 26 | 1.000 | d=1, T^{*} M | | |
| cardona-qft-methods_FO0349 | 26 | 1.000 | \sigma_{-d}^{P}=0 | | |
| cardona-qft-methods_FO0350 | 26 | 1.000 | \sigma^{P}(x, \xi) | | |
| cardona-qft-methods_FO0351 | 26 | 0.998 | \sigma^{P} \simeq \sum_{j} \sigma_{m-j}^{P} | | |
| cardona-qft-methods_FO0352 | 26 | 0.998 | m=\operatorname{order}(P) | | |
| cardona-qft-methods_FO0353 | 26 | 1.000 | \sum_{k=1}^{d} \xi_{k} \partial_{\xi_{k}} \sigma_{m-j}^{P}=(m-j) \sigma_{m-j}^{P} | | |
| cardona-qft-methods_FO0354 | 26 | 1.000 | m=j! | | |
| cardona-qft-methods_FO0355 | 26 | 1.000 | \sum_{k=1}^{d}\left[x^{k}, \xi_{k} \sigma_{m-j}^{P}\right]=i \sum_{k=1}^{d} \partial_{\xi_{k}} \xi_{k} \sigma_{m-j}^{P}=i(m-j+d) \sigma_{m-j}^{P} | | |
| cardona-qft-methods_FO0356 | 26 | 1.000 | \sigma^{P}= | | |
| cardona-qft-methods_FO0357 | 26 | 1.000 | \sum_{k=1}^{d}\left[\xi_{k} \tau, x^{k}\right] | | |
| cardona-qft-methods_FO0358 | 26 | 1.000 | T | | |
| cardona-qft-methods_FO0359 | 26 | 1.000 | T(P) | | |
| cardona-qft-methods_FO0360 | 26 | 1.000 | \sigma_{-d}^{P} | | |
| cardona-qft-methods_FO0361 | 26 | 1.000 | T([\cdot, \cdot])=0 | | |
| cardona-qft-methods_FO0362 | 26 | 1.000 | \int_{\mathbb{S}^{d-1}} \sigma_{-d}^{P}(x, \xi) d|\xi|=0 | | |
| cardona-qft-methods_FO0363 | 26 | 1.000 | \Delta_{\mathbb{S}} f=0 \Longleftrightarrow | | |
| cardona-qft-methods_FO0364 | 26 | 0.987 | d f=0 \Longleftrightarrow f=c s t | | |
| cardona-qft-methods_FO0365 | 26 | 0.987 | \Delta_{\mathbb{S}^{d-1}} h=\sigma_{-d \mid \mathbb{S}^{d-1}}^{P} | | |
| cardona-qft-methods_FO0366 | 26 | 0.987 | h | | |
| cardona-qft-methods_FO0367 | 26 | 1.000 | \tilde{h}(\xi)=|\xi|^{-d+2} h\left(\frac{\xi}{|\xi|}\right) | | |
| cardona-qft-methods_FO0368 | 26 | 1.000 | \Delta_{\mathbb{R}^{d}} \tilde{h}(\xi)= | | |
| cardona-qft-methods_FO0369 | 26 | 1.000 | |\xi| \sigma_{-d}^{P}\left(\frac{\xi}{|\xi|}\right)=\sigma_{-d}^{P}(\xi) | | |
| cardona-qft-methods_FO0370 | 26 | 1.000 | \Delta_{\mathbb{R}^{d}}=r^{1-d} \partial_{r}\left(r^{d-1} \partial_{r}\right)+r^{-2} \Delta_{\mathbb{S}^{d-1}} | | |
| cardona-qft-methods_FO0371 | 26 | 1.000 | \tilde{h} | | |
| cardona-qft-methods_FO0372 | 26 | 1.000 | d-2 | | |
| cardona-qft-methods_FO0373 | 26 | 1.000 | \partial_{\xi} \tilde{h} | | |
| cardona-qft-methods_FO0374 | 26 | 1.000 | d-1 | | |
| cardona-qft-methods_FO0375 | 26 | 1.000 | \sigma_{-d}^{P}(x, \xi)-\frac{|\xi|^{-d}}{\operatorname{Vol}\left(\mathbb{S}^{d-1}\right)} c_{P}(x) | | |
| cardona-qft-methods_FO0376 | 26 | 1.000 | -d | | |
| cardona-qft-methods_FO0377 | 26 | 1.000 | T(P)= | | |
| cardona-qft-methods_FO0378 | 26 | 1.000 | T\left(O p\left(|\xi|^{-d} c_{p}(x)\right), \forall T \in \Psi D O^{\mathbb{Z}}(M, E)\right. | | |
| cardona-qft-methods_FO0379 | 26 | 1.000 | \mu: f \in C_{c}^{\infty}(U) \rightarrow | | |
| cardona-qft-methods_FO0380 | 26 | 1.000 | T\left(O p\left(f|\xi|^{-d}\right)\right) | | |
| cardona-qft-methods_FO0381 | 26 | 1.000 | \mu\left(\partial_{x^{k}} f\right)=0 | | |
| cardona-qft-methods_FO0382 | 27 | 1.000 | \partial_{x^{k}}(f)|\xi|^{-d} | | |
| cardona-qft-methods_FO0383 | 27 | 1.000 | \mu | | |
| cardona-qft-methods_FO0384 | 27 | 1.000 | (1+\Delta)^{-d / 2} \in \Psi D O(M) | | |
| cardona-qft-methods_FO0385 | 27 | 1.000 | \sigma_{-d}^{(1+\Delta)^{-d / 2}} | | |
| cardona-qft-methods_FO0386 | 27 | 1.000 | \sigma_{-d}^{(1+\Delta)^{-d / 2}}(x, \xi)=-\left(g_{x}^{i j} \xi_{i} \xi_{j}\right)^{-d / 2}=-\|\xi\|_{x}^{-d} | | |
| cardona-qft-methods_FO0387 | 27 | 0.675 | { }^{33,49,68,87,104,105} | | |
| cardona-qft-methods_FO0388 | 27 | 1.000 | \mathcal{B}(\mathcal{H}) | | |
| cardona-qft-methods_FO0389 | 27 | 1.000 | \omega | | |
| cardona-qft-methods_FO0390 | 27 | 1.000 | \mathcal{M} | | |
| cardona-qft-methods_FO0391 | 27 | 1.000 | \mathcal{M}^{+}=\left\{a a^{*} \mid a \in \mathcal{M}\right\} | | |
| cardona-qft-methods_FO0392 | 27 | 1.000 | [0, \infty] | | |
| cardona-qft-methods_FO0393 | 27 | 0.788 | \omega \in \mathcal{M}^{*} | | |
| cardona-qft-methods_FO0394 | 27 | 0.788 | \omega(a)<\infty, \forall a \in \mathcal{M} | | |
| cardona-qft-methods_FO0395 | 27 | 0.788 | \omega(1)=1 | | |
| cardona-qft-methods_FO0396 | 27 | 1.000 | \omega\left(a a^{*}\right)=\omega\left(a^{*} a\right) | | |
| cardona-qft-methods_FO0397 | 27 | 1.000 | a \in \mathcal{M} | | |
| cardona-qft-methods_FO0398 | 27 | 0.993 | \omega\left(\sup _{\alpha} a_{\alpha}\right)=\sup _{\alpha} \omega\left(a_{\alpha}\right) | | |
| cardona-qft-methods_FO0399 | 27 | 0.993 | \left(a_{\alpha}\right) \subset \mathcal{M}^{+} | | |
| cardona-qft-methods_FO0400 | 27 | 1.000 | \left(a_{\alpha}\right)_{\alpha} | | |
| cardona-qft-methods_FO0401 | 28 | 0.628 | \operatorname{Tr}_{\text {Dix }}(T) "=" \lim _{N \rightarrow \infty} \frac{1}{\log N} \sum_{n=0}^{N} \mu_{n}(T) | | |
| cardona-qft-methods_FO0402 | 28 | 0.628 | \mu_{n}(T) | | |
| cardona-qft-methods_FO0403 | 28 | 0.988 | P \in \Psi D O^{-d}(M) | | |
| cardona-qft-methods_FO0404 | 28 | 1.000 | S^{*} M | | |
| cardona-qft-methods_FO0405 | 28 | 1.000 | \sum_{n \in \mathbb{N}^{*}} \frac{1}{n} | | |
| cardona-qft-methods_FO0406 | 28 | 1.000 | \frac{1}{r} | | |
| cardona-qft-methods_FO0407 | 28 | 1.000 | \zeta: s \in \mathbb{C} \rightarrow \sum_{n \in \mathbb{N}^{*}} \frac{1}{n^{s}} | | |
| cardona-qft-methods_FO0408 | 28 | 1.000 | \zeta_{P}(s)=\operatorname{Tr}\left(P|\mathcal{D}|^{-s}\right) | | |
| cardona-qft-methods_FO0409 | 28 | 1.000 | T \in \mathcal{K}(\mathcal{H}) | | |
| cardona-qft-methods_FO0410 | 28 | 1.000 | \mu_{n}(T)= | | |
| cardona-qft-methods_FO0411 | 28 | 0.707 | \inf \left\{\left\|T_{\left\lceil E^{\perp}\right.}\right\| \mid E\right. | | |
| cardona-qft-methods_FO0412 | 28 | 0.707 | \left.\operatorname{dim}(E)=n\right\}, n \in \mathbb{N} | | |
| cardona-qft-methods_FO0413 | 28 | 1.000 | (n+1) | | |
| cardona-qft-methods_FO0414 | 28 | 1.000 | |T| | | |
| cardona-qft-methods_FO0415 | 28 | 1.000 | \lim _{n \rightarrow \infty} \mu_{n}(T)=0 | | |
| cardona-qft-methods_FO0416 | 28 | 1.000 | \epsilon>0 | | |
| cardona-qft-methods_FO0417 | 28 | 0.933 | E_{\epsilon} | | |
| cardona-qft-methods_FO0418 | 28 | 0.933 | \left\|T_{\uparrow E_{\epsilon}^{\perp}}\right\|<\epsilon | | |
| cardona-qft-methods_FO0419 | 28 | 1.000 | N \in \mathbb{N} | | |
| cardona-qft-methods_FO0420 | 28 | 1.000 | \sigma_{N}(T)=\sum_{n=0}^{N} \mu_{n}(T) | | |
| cardona-qft-methods_FO0421 | 29 | 0.999 | \|T\| \leq \sigma_{N}(T) \leq N\|T\| | | |
| cardona-qft-methods_FO0422 | 29 | 0.999 | \sigma_{n} \simeq\|\cdot\| | | |
| cardona-qft-methods_FO0423 | 29 | 0.999 | \mathcal{K}(\mathcal{H}) | | |
| cardona-qft-methods_FO0424 | 29 | 1.000 | \sigma_{N} | | |
| cardona-qft-methods_FO0425 | 29 | 1.000 | \lambda \in \mathbb{R}^{+} | | |
| cardona-qft-methods_FO0426 | 29 | 1.000 | \sigma_{\lambda_{1}}\left(T_{1}\right)+\sigma_{\lambda_{2}}\left(T_{2}\right)=\sigma_{\lambda_{1}+\lambda_{2}}\left(T_{1}+T_{2}\right) | | |
| cardona-qft-methods_FO0427 | 29 | 1.000 | \lambda_{1}, \lambda_{2} \in \mathbb{R}^{+}, 0 \leq | | |
| cardona-qft-methods_FO0428 | 29 | 0.996 | T_{1}, T_{2} \in \mathcal{K}(\mathcal{H}) | | |
| cardona-qft-methods_FO0429 | 29 | 1.000 | \mathcal{L}^{p}(\mathcal{H}) | | |
| cardona-qft-methods_FO0430 | 29 | 1.000 | \operatorname{Tr}\left(|T|^{p}\right)<\infty | | |
| cardona-qft-methods_FO0431 | 29 | 1.000 | \sigma_{\lambda}(T)= | | |
| cardona-qft-methods_FO0432 | 29 | 1.000 | \mathcal{O}\left(\lambda^{1-1 / p}\right) | | |
| cardona-qft-methods_FO0433 | 29 | 1.000 | \mathcal{L}^{1, \infty} | | |
| cardona-qft-methods_FO0434 | 29 | 1.000 | C^{*} | | |
| cardona-qft-methods_FO0435 | 29 | 1.000 | \|\cdot\|_{1, \infty} | | |
| cardona-qft-methods_FO0436 | 29 | 1.000 | \frac{\sigma_{\rho}(T)}{\log \rho} | | |
| cardona-qft-methods_FO0437 | 29 | 1.000 | \mathbb{R}_{+}^{*} | | |
| cardona-qft-methods_FO0438 | 29 | 0.997 | \lambda \geq e | | |
| cardona-qft-methods_FO0439 | 29 | 0.997 | \tau_{\lambda}(T)=\frac{1}{\log \lambda} \int_{e}^{\lambda} \frac{\sigma_{\rho}(T)}{\log \rho} \frac{d \rho}{\rho} | | |
| cardona-qft-methods_FO0440 | 29 | 1.000 | \sigma_{\rho}(T) \leq \log \rho\|T\|_{1, \infty} | | |
| cardona-qft-methods_FO0441 | 29 | 1.000 | \tau_{\lambda}(T) \leq\|T\|_{1, \infty} | | |
| cardona-qft-methods_FO0442 | 29 | 1.000 | \lambda \rightarrow | | |
| cardona-qft-methods_FO0443 | 29 | 1.000 | \tau_{\lambda}(T) | | |
| cardona-qft-methods_FO0444 | 29 | 1.000 | C_{b}([e, \infty]) | | |
| cardona-qft-methods_FO0445 | 29 | 0.905 | T_{1}, T_{2} \in \mathcal{L}_{+}^{1, \infty} | | |
| cardona-qft-methods_FO0446 | 30 | 1.000 | \lambda \rightarrow \tau_{\lambda}(T) | | |
| cardona-qft-methods_FO0447 | 30 | 1.000 | \lambda \rightarrow\left(\frac{\log 2(2+\log \log \lambda)}{\log \lambda}\right) | | |
| cardona-qft-methods_FO0448 | 30 | 1.000 | C_{0}([e, \infty[) | | |
| cardona-qft-methods_FO0449 | 30 | 1.000 | \mathcal{A}=C_{b}([e, \infty]) / C_{0}([e, \infty[) | | |
| cardona-qft-methods_FO0450 | 30 | 1.000 | [\tau(T)] | | |
| cardona-qft-methods_FO0451 | 30 | 1.000 | [\tau]: T \rightarrow[\tau(T)] | | |
| cardona-qft-methods_FO0452 | 30 | 1.000 | \mathcal{L}_{+}^{1, \infty} | | |
| cardona-qft-methods_FO0453 | 30 | 1.000 | \left[\tau\left(U T U^{*}\right)\right]=[\tau(T)] | | |
| cardona-qft-methods_FO0454 | 30 | 0.902 | \omega \circ[\tau(\cdot)] | | |
| cardona-qft-methods_FO0455 | 30 | 0.902 | C^{*}- | | |
| cardona-qft-methods_FO0456 | 30 | 0.915 | \omega \circ[\tau(\cdot)]: T \in \mathcal{L}^{1, \infty} \rightarrow | | |
| cardona-qft-methods_FO0457 | 30 | 0.976 | \omega([\tau(T)]) \in \mathbb{C} | | |
| cardona-qft-methods_FO0458 | 30 | 0.976 | \omega\left(\left[\tau\left(T_{1} T_{2}\right)\right]\right)=\omega\left(\left[\tau\left(T_{2} T_{1}\right)\right]\right) | | |
| cardona-qft-methods_FO0459 | 30 | 0.976 | T_{1}, T_{2} \in \mathcal{L}^{1, \infty} | | |
| cardona-qft-methods_FO0460 | 30 | 1.000 | \operatorname{Tr}_{\omega} | | |
| cardona-qft-methods_FO0461 | 30 | 1.000 | \operatorname{Tr}_{\omega}(\cdot)=\omega \circ[\tau(\cdot)] | | |
| cardona-qft-methods_FO0462 | 30 | 1.000 | \operatorname{Tr}_{\omega}(T)=0 | | |
| cardona-qft-methods_FO0463 | 30 | 1.000 | T \in \mathcal{L}^{1}(\mathcal{H}) | | |
| cardona-qft-methods_FO0464 | 30 | 1.000 | \|.\|_{1, \infty} | | |
| cardona-qft-methods_FO0465 | 30 | 1.000 | p \geq 1, \mathcal{L}^{1, \infty} | | |
| cardona-qft-methods_FO0466 | 30 | 1.000 | f \in C_{b}([e, \infty]) | | |
| cardona-qft-methods_FO0467 | 30 | 1.000 | \ell=\lim _{\lambda \rightarrow \infty} f(\lambda) | | |
| cardona-qft-methods_FO0468 | 30 | 1.000 | \ell=\omega(f) | | |
| cardona-qft-methods_FO0469 | 30 | 1.000 | T \in \mathcal{L}^{1, \infty} | | |
| cardona-qft-methods_FO0470 | 30 | 1.000 | \operatorname{Tr}_{\omega}(T) | | |
| cardona-qft-methods_FO0471 | 30 | 1.000 | \operatorname{Tr}_{\text {Dix }} | | |
| cardona-qft-methods_FO0472 | 30 | 1.000 | \operatorname{Tr}_{\omega}(T)=\ell | | |
| cardona-qft-methods_FO0473 | 30 | 1.000 | \lambda \in \mathbb{R}^{+} \rightarrow \tau_{\lambda}(T) \in \mathcal{A} | | |
| cardona-qft-methods_FO0474 | 30 | 1.000 | \ell | | |
| cardona-qft-methods_FO0475 | 30 | 1.000 | { }^{72,74,75} | | |
| cardona-qft-methods_FO0476 | 30 | 1.000 | T \in \mathcal{K}_{+}(\mathcal{H}) | | |
| cardona-qft-methods_FO0477 | 30 | 1.000 | \lim _{N \rightarrow \infty} \frac{1}{\log N} \sum_{n=0}^{N} \mu_{n}(T) | | |
| cardona-qft-methods_FO0478 | 31 | 1.000 | \mathbb{T}^{d}=\mathbb{R}^{d} / 2 \pi \mathbb{Z}^{d} | | |
| cardona-qft-methods_FO0479 | 31 | 1.000 | \Delta=-\sum_{i=1}^{d} \partial_{x^{i}}^{2} | | |
| cardona-qft-methods_FO0480 | 31 | 0.997 | \mathcal{H}=L^{2}\left(\mathbb{T}^{d}\right) | | |
| cardona-qft-methods_FO0481 | 31 | 1.000 | \operatorname{Tr}_{\omega}\left((1+\Delta)^{-p}\right) | | |
| cardona-qft-methods_FO0482 | 31 | 1.000 | \frac{d}{2} \leq p \in \mathbb{N}^{*} | | |
| cardona-qft-methods_FO0483 | 31 | 1.000 | 1+\Delta | | |
| cardona-qft-methods_FO0484 | 31 | 1.000 | \epsilon | | |
| cardona-qft-methods_FO0485 | 31 | 1.000 | e_{k}(x)=\frac{1}{2 \pi} e^{i k \cdot x} | | |
| cardona-qft-methods_FO0486 | 31 | 1.000 | x \in \mathbb{T}^{d}, k \in \mathbb{Z}^{d}= | | |
| cardona-qft-methods_FO0487 | 31 | 1.000 | \left(\mathbb{T}^{d}\right)^{*} | | |
| cardona-qft-methods_FO0488 | 31 | 1.000 | \Delta e_{k}=|k|^{2} e_{k} | | |
| cardona-qft-methods_FO0489 | 31 | 1.000 | t \in | | |
| cardona-qft-methods_FO0490 | 31 | 1.000 | \mathbb{R}_{+}^{*}, e^{t} \operatorname{Tr}\left(e^{-t(1+\Delta)}\right)=\sum_{k \in \mathbb{Z}^{d}} e^{-t|k|^{2}}=\left(\sum_{k \in \mathbb{Z}} e^{-t k^{2}}\right)^{d} | | |
| cardona-qft-methods_FO0491 | 31 | 1.000 | \left|\int_{-\infty}^{\infty} e^{-t x^{2}} d x-\sum_{k \in \mathbb{Z}} e^{-t k^{2}}\right| \leq 1 | | |
| cardona-qft-methods_FO0492 | 31 | 1.000 | \sqrt{\frac{\pi}{t}} | | |
| cardona-qft-methods_FO0493 | 31 | 0.953 | e^{t} \operatorname{Tr}\left(e^{-t(1+\Delta)}\right) \underset{t \downarrow 0^{+}}{\sim}\left(\frac{\pi}{t}\right)^{d / 2}=\alpha t^{-d / 2} | | |
| cardona-qft-methods_FO0494 | 31 | 0.995 | \left.\mu_{n}\left((1+\Delta)^{-d / 2}\right)\right) \underset{n \rightarrow \infty}{\simeq}\left(\alpha \frac{1}{\Gamma(d / 2+1)}\right) \frac{1}{n} | | |
| cardona-qft-methods_FO0495 | 31 | 1.000 | { }^{49,54} | | |
| cardona-qft-methods_FO0496 | 31 | 1.000 | (1+\Delta)^{-d / 2} | | |
| cardona-qft-methods_FO0497 | 31 | 1.000 | \left.\operatorname{Tr}_{\text {Dix }}\left((1+\Delta)^{-d / 2}\right)\right)=\operatorname{Tr}_{\omega}((1+ | | |
| cardona-qft-methods_FO0498 | 31 | 0.997 | \left.\left.\Delta)^{-d / 2}\right)\right)=\frac{\pi^{d / 2}}{\Gamma(d / 2+1)} | | |
| cardona-qft-methods_FO0499 | 31 | 0.997 | (1+\Delta)^{-p} | | |
| cardona-qft-methods_FO0500 | 31 | 0.997 | p>\frac{d}{2}, \operatorname{Tr}_{\text {Dix }}((1+ | | |
| cardona-qft-methods_FO0501 | 31 | 0.843 | \left.\Delta)^{-p}\right)=0 | | |
| cardona-qft-methods_FO0502 | 31 | 1.000 | P \in \Psi D O^{-d}(M, E) | | |
| cardona-qft-methods_FO0503 | 31 | 1.000 | P \in \mathcal{L}^{1, \infty} | | |
| cardona-qft-methods_FO0504 | 31 | 1.000 | \operatorname{Tr}_{\text {Dix }}(P)=\frac{1}{d} W \operatorname{Res}(P) | | |
| cardona-qft-methods_FO0505 | 31 | 1.000 | { }^{c} | | |
| cardona-qft-methods_FO0506 | 31 | 1.000 | C(M) | | |
| cardona-qft-methods_FO0507 | 31 | 1.000 | \Gamma(\mathcal{C} \ell M) | | |
| cardona-qft-methods_FO0508 | 32 | 1.000 | E=\mathcal{C} \ell T^{*} M | | |
| cardona-qft-methods_FO0509 | 32 | 1.000 | T_{x}^{*} M | | |
| cardona-qft-methods_FO0510 | 32 | 0.611 | m \in \mathbb{N} | | |
| cardona-qft-methods_FO0511 | 32 | 0.611 | \operatorname{Diff}^{m}(M, E)=\Gamma(M, \operatorname{End}(E)) \cdot | | |
| cardona-qft-methods_FO0512 | 32 | 0.989 | \left\{\nabla_{X_{1}} \cdots \nabla_{X_{j}} \mid X_{j} \in \Gamma(M, T M), j \leq m\right\} | | |
| cardona-qft-methods_FO0513 | 32 | 1.000 | \operatorname{Diff}^{m}(M, E) | | |
| cardona-qft-methods_FO0514 | 32 | 1.000 | \operatorname{End}(\Gamma(M, E)) | | |
| cardona-qft-methods_FO0515 | 32 | 0.980 | \Gamma\left(T^{*} M, \pi^{*} \operatorname{End}(E)\right) | | |
| cardona-qft-methods_FO0516 | 32 | 0.980 | \pi | | |
| cardona-qft-methods_FO0517 | 32 | 1.000 | E=\wedge T^{*} M | | |
| cardona-qft-methods_FO0518 | 32 | 1.000 | \omega, \omega_{j} \in E | | |
| cardona-qft-methods_FO0519 | 32 | 1.000 | c(\omega)=\epsilon(\omega)+\iota(\omega) | | |
| cardona-qft-methods_FO0520 | 32 | 1.000 | e_{1}, \cdots, e_{d} | | |
| cardona-qft-methods_FO0521 | 32 | 1.000 | e_{i_{1}} \wedge \cdots \wedge e_{i_{p}} | | |
| cardona-qft-methods_FO0522 | 32 | 1.000 | i_{1}<\cdots<i_{p} | | |
| cardona-qft-methods_FO0523 | 32 | 1.000 | d \in | | |
| cardona-qft-methods_FO0524 | 32 | 1.000 | ^{1} | | |
| cardona-qft-methods_FO0525 | 32 | 1.000 | d^{*} | | |
| cardona-qft-methods_FO0526 | 32 | 1.000 | \Gamma(M, E) | | |
| cardona-qft-methods_FO0527 | 32 | 1.000 | \sigma_{1}^{d}(x, \xi)=i \xi | | |
| cardona-qft-methods_FO0528 | 32 | 1.000 | \sigma_{1}^{d^{*}} | | |
| cardona-qft-methods_FO0529 | 32 | 1.000 | P \in \operatorname{Diff}^{m}(M) | | |
| cardona-qft-methods_FO0530 | 32 | 1.000 | \sigma_{m}^{P}(d h)=\frac{1}{i^{m} m!}(a d h)^{m}(P) | | |
| cardona-qft-methods_FO0531 | 32 | 0.901 | a d h=[\cdot, h] | | |
| cardona-qft-methods_FO0532 | 32 | 0.901 | \sigma_{m}^{P^{*}}(\omega)=\sigma_{m}^{P}(\omega)^{*} | | |
| cardona-qft-methods_FO0533 | 32 | 0.901 | P^{*} | | |
| cardona-qft-methods_FO0534 | 32 | 1.000 | E:\left\langle\psi, \psi^{\prime}\right\rangle= | | |
| cardona-qft-methods_FO0535 | 32 | 1.000 | \int_{M}\left\langle\psi(x), \psi^{\prime}(x)\right\rangle_{x}|d x| | | |
| cardona-qft-methods_FO0536 | 32 | 1.000 | P \in \operatorname{Diff}^{2}(M, E) | | |
| cardona-qft-methods_FO0537 | 32 | 1.000 | \sigma_{2}^{P}(x, \xi)=|\xi|_{x}^{2} i d_{E_{x}} | | |
| cardona-qft-methods_FO0538 | 32 | 1.000 | x \in M, \xi \in | | |
| cardona-qft-methods_FO0539 | 33 | 1.000 | P= | | |
| cardona-qft-methods_FO0540 | 33 | 1.000 | -\sum_{i, j} g^{i j}(x) \partial_{x^{i}} \partial_{x^{j}}+b^{j}(x) \partial_{x^{j}}+c(x) | | |
| cardona-qft-methods_FO0541 | 33 | 1.000 | b^{j} | | |
| cardona-qft-methods_FO0542 | 33 | 0.981 | \Gamma(M, \operatorname{End}(E)) | | |
| cardona-qft-methods_FO0543 | 33 | 1.000 | E=E^{+} \oplus E^{-} | | |
| cardona-qft-methods_FO0544 | 33 | 1.000 | \mathbb{Z}_{2} | | |
| cardona-qft-methods_FO0545 | 33 | 1.000 | D \in \operatorname{Diff}^{1}(M, E) | | |
| cardona-qft-methods_FO0546 | 33 | 1.000 | D=\left(\begin{array}{cc}0 & D^{+} \\ D^{-} & 0\end{array}\right) | | |
| cardona-qft-methods_FO0547 | 33 | 1.000 | D | | |
| cardona-qft-methods_FO0548 | 33 | 0.992 | D^{ \pm}: \Gamma\left(M, E^{\mp}\right) \rightarrow \Gamma\left(M, E^{ \pm}\right), D | | |
| cardona-qft-methods_FO0549 | 33 | 0.992 | D^{2}= | | |
| cardona-qft-methods_FO0550 | 33 | 1.000 | \left(\begin{array}{cc}D^{-} D^{+} & 0 \\ 0 & D^{+} D^{-}\end{array}\right) | | |
| cardona-qft-methods_FO0551 | 33 | 0.370 | E=\wedge T^{*} M=\wedge^{\text {even }} T^{*} M \oplus \bigwedge^{\text {odd }} T^{*} M | | |
| cardona-qft-methods_FO0552 | 33 | 1.000 | D=d+d^{*} | | |
| cardona-qft-methods_FO0553 | 33 | 1.000 | D^{2}=d d^{*}+d^{*} d | | |
| cardona-qft-methods_FO0554 | 33 | 1.000 | D^{2} | | |
| cardona-qft-methods_FO0555 | 33 | 1.000 | \mathcal{C} \ell M | | |
| cardona-qft-methods_FO0556 | 33 | 1.000 | \mathcal{C} \ell T_{x} M | | |
| cardona-qft-methods_FO0557 | 33 | 1.000 | X \in T M \leftrightarrow X^{b} \in T^{*} M | | |
| cardona-qft-methods_FO0558 | 33 | 1.000 | c: \Gamma(M, \mathcal{C} \ell M) \rightarrow \operatorname{End}(\Gamma(M, E)) | | |
| cardona-qft-methods_FO0559 | 33 | 0.997 | D \in \operatorname{Diff}^{1} | | |
| cardona-qft-methods_FO0560 | 33 | 1.000 | [D, f]=i c(d f) | | |
| cardona-qft-methods_FO0561 | 33 | 1.000 | f \in C^{\infty}(M) | | |
| cardona-qft-methods_FO0562 | 33 | 1.000 | c(d f)=-i[D, f] | | |
| cardona-qft-methods_FO0563 | 33 | 1.000 | c=i(\epsilon+\iota) | | |
| cardona-qft-methods_FO0564 | 33 | 1.000 | a \in \Gamma(M, \mathcal{C} \ell M) | | |
| cardona-qft-methods_FO0565 | 33 | 1.000 | X \in \Gamma(M, T M) | | |
| cardona-qft-methods_FO0566 | 33 | 1.000 | \left[\nabla_{X}, c(a)\right]=c\left(\nabla_{X}^{L C} a\right) | | |
| cardona-qft-methods_FO0567 | 33 | 1.000 | \nabla_{X}^{L C} | | |
| cardona-qft-methods_FO0568 | 33 | 1.000 | D_{\nabla} | | |
| cardona-qft-methods_FO0569 | 33 | 1.000 | c \otimes 1 | | |
| cardona-qft-methods_FO0570 | 34 | 1.000 | \nabla=\sum_{j=1}^{d} d x^{j} \otimes \nabla_{\partial_{j}} | | |
| cardona-qft-methods_FO0571 | 34 | 1.000 | D_{\nabla}=-i \sum_{j} c\left(d x^{j}\right) \nabla_{\partial_{i}} | | |
| cardona-qft-methods_FO0572 | 34 | 0.529 | \left[D_{\nabla}, f i d_{E}\right]=-i \sum_{i=1}^{d} c\left(d x^{i}\right)\left[\nabla_{\partial_{j}}, f\right]=\sum_{j=1}^{d}-i c\left(d x^{j}\right) \partial_{j} f=-i c(d f) | | |
| cardona-qft-methods_FO0573 | 34 | 1.000 | \operatorname{Spin}_{d} | | |
| cardona-qft-methods_FO0574 | 34 | 1.000 | S O_{d} | | |
| cardona-qft-methods_FO0575 | 34 | 1.000 | 0 \longrightarrow \mathbb{Z}_{2} \longrightarrow \operatorname{Spin}_{d} \xrightarrow{\xi} S O_{d} \longrightarrow 1 | | |
| cardona-qft-methods_FO0576 | 34 | 0.999 | \mathrm{SO}(T M) \rightarrow M | | |
| cardona-qft-methods_FO0577 | 34 | 0.999 | \mathrm{SO}_{d} | | |
| cardona-qft-methods_FO0578 | 34 | 1.000 | T M | | |
| cardona-qft-methods_FO0579 | 34 | 0.901 | \operatorname{Spin}(T M) \xrightarrow{\pi} M | | |
| cardona-qft-methods_FO0580 | 34 | 0.608 | \operatorname{Spin}(T M) \xrightarrow{\eta} \operatorname{SO}(T M) | | |
| cardona-qft-methods_FO0581 | 34 | 0.999 | \operatorname{Spin}(T M) | | |
| cardona-qft-methods_FO0582 | 34 | 0.999 | \operatorname{SO}(T M) | | |
| cardona-qft-methods_FO0583 | 34 | 1.000 | \operatorname{Spin}_{d}^{c} | | |
| cardona-qft-methods_FO0584 | 34 | 0.999 | \mathbb{T}: 0 \longrightarrow \mathbb{T} \longrightarrow \operatorname{Spin}_{d}^{c} \xrightarrow{\xi} S O_{d} \longrightarrow 1 | | |
| cardona-qft-methods_FO0585 | 34 | 0.972 | M, g | | |
| cardona-qft-methods_FO0586 | 34 | 1.000 | H^{1}\left(M, \mathbb{Z}_{2}\right) | | |
| cardona-qft-methods_FO0587 | 34 | 1.000 | \rho | | |
| cardona-qft-methods_FO0588 | 34 | 1.000 | \mathcal{C} \ell \mathbb{C}^{d} \rightarrow \operatorname{End}_{\mathbb{C}}\left(\Sigma_{d}\right) | | |
| cardona-qft-methods_FO0589 | 34 | 1.000 | \Sigma_{d} \simeq | | |
| cardona-qft-methods_FO0590 | 34 | 0.999 | \mathbb{C}^{2^{\lfloor d / 2\rfloor}} | | |
| cardona-qft-methods_FO0591 | 34 | 0.999 | \mathcal{C} \ell \mathbb{C}^{d} | | |
| cardona-qft-methods_FO0592 | 34 | 1.000 | S | | |
| cardona-qft-methods_FO0593 | 35 | 1.000 | S=\operatorname{Spin}(T M) \times_{\rho_{d}} \Sigma_{d} | | |
| cardona-qft-methods_FO0594 | 35 | 1.000 | \rho_{d} | | |
| cardona-qft-methods_FO0595 | 35 | 1.000 | \operatorname{Aut}\left(\Sigma_{d}\right) | | |
| cardona-qft-methods_FO0596 | 35 | 1.000 | d=2 m | | |
| cardona-qft-methods_FO0597 | 35 | 1.000 | \rho_{d}=\rho^{+}+\rho^{-} | | |
| cardona-qft-methods_FO0598 | 35 | 1.000 | \rho^{ \pm} | | |
| cardona-qft-methods_FO0599 | 35 | 1.000 | \operatorname{Spin}_{2 m} | | |
| cardona-qft-methods_FO0600 | 35 | 1.000 | \Sigma_{2 m}= | | |
| cardona-qft-methods_FO0601 | 35 | 1.000 | \Sigma_{2 m}^{+} \oplus \Sigma_{2 m}^{-} | | |
| cardona-qft-methods_FO0602 | 35 | 1.000 | d=2 m+1 | | |
| cardona-qft-methods_FO0603 | 35 | 0.798 | S=S^{+} \oplus S^{-} | | |
| cardona-qft-methods_FO0604 | 35 | 0.798 | S \simeq \bigwedge T^{*} M | | |
| cardona-qft-methods_FO0605 | 35 | 1.000 | S \simeq M \times \mathbb{C}^{d / 2} | | |
| cardona-qft-methods_FO0606 | 35 | 0.974 | \nabla^{S}: \Gamma^{\infty}(M, S) \rightarrow \Gamma^{\infty}(M, S) \otimes \Gamma^{\infty}\left(M, T^{*} M\right) | | |
| cardona-qft-methods_FO0607 | 35 | 0.977 | \left[\nabla^{S}, c(\cdot)\right]=c\left(\nabla^{L C} \cdot\right) | | |
| cardona-qft-methods_FO0608 | 35 | 1.000 | \not D=-i c\left(d x^{j}\right)\left(\partial_{j}-\omega_{j}(x)\right) | | |
| cardona-qft-methods_FO0609 | 35 | 1.000 | \omega_{j} | | |
| cardona-qft-methods_FO0610 | 35 | 1.000 | \omega_{j}=\frac{1}{4}\left(\Gamma_{j i}^{k} g_{k l}-\right. | | |
| cardona-qft-methods_FO0611 | 35 | 1.000 | \left.\partial_{i}\left(h_{j}^{\alpha}\right) \delta_{\alpha \beta} h_{l}^{\beta}\right) c\left(d x^{i}\right) c\left(d x^{l}\right) | | |
| cardona-qft-methods_FO0612 | 35 | 1.000 | H=\left[h_{j}^{\alpha}\right] | | |
| cardona-qft-methods_FO0613 | 35 | 1.000 | H^{t} H= | | |
| cardona-qft-methods_FO0614 | 35 | 1.000 | \left[g_{i j}\right] | | |
| cardona-qft-methods_FO0615 | 35 | 1.000 | \sigma_{1}^{D}(x, \xi)=c(\xi)+i c\left(d x^{j}\right) \omega_{j}(x) | | |
| cardona-qft-methods_FO0616 | 35 | 1.000 | x_{0} | | |
| cardona-qft-methods_FO0617 | 35 | 1.000 | \gamma | | |
| cardona-qft-methods_FO0618 | 35 | 0.999 | C^{\infty}(M) | | |
| cardona-qft-methods_FO0619 | 35 | 1.000 | \Gamma^{\infty}(M, S), \not D | | |
| cardona-qft-methods_FO0620 | 35 | 1.000 | \langle\psi, \not D \phi\rangle=\langle\not D \psi, \phi\rangle | | |
| cardona-qft-methods_FO0621 | 35 | 0.719 | \not D^{* *} | | |
| cardona-qft-methods_FO0622 | 36 | 0.919 | \mathcal{H}, \not D | | |
| cardona-qft-methods_FO0623 | 36 | 1.000 | \Gamma^{\infty}(M, S) | | |
| cardona-qft-methods_FO0624 | 36 | 1.000 | \not D | | |
| cardona-qft-methods_FO0625 | 36 | 1.000 | R \in \Gamma^{\infty}\left(M, \bigwedge^{2} T^{*} M \otimes\right. | | |
| cardona-qft-methods_FO0626 | 36 | 0.785 | \operatorname{End}(T M)) | | |
| cardona-qft-methods_FO0627 | 36 | 0.785 | R_{i j k l}= | | |
| cardona-qft-methods_FO0628 | 36 | 1.000 | g\left(\partial_{i}, R\left(\partial_{k}, \partial_{l}\right) \partial_{j}\right) | | |
| cardona-qft-methods_FO0629 | 36 | 1.000 | R_{j l}=g^{i k} T_{i j k l} | | |
| cardona-qft-methods_FO0630 | 36 | 1.000 | s=g^{j l} R_{j l} | | |
| cardona-qft-methods_FO0631 | 36 | 1.000 | M, \not D^{2}=\Delta^{S}+\frac{1}{4} s | | |
| cardona-qft-methods_FO0632 | 36 | 1.000 | \not D^{-1} | | |
| cardona-qft-methods_FO0633 | 36 | 1.000 | \left\{\lambda_{n}(T)\right\}_{n \in \mathbb{N}} | | |
| cardona-qft-methods_FO0634 | 36 | 1.000 | T^{-1} | | |
| cardona-qft-methods_FO0635 | 36 | 1.000 | N_{T}(\lambda)= | | |
| cardona-qft-methods_FO0636 | 36 | 0.996 | \#\left\{\lambda_{n}(T) \mid \lambda_{n} \leq \lambda\right\} | | |
| cardona-qft-methods_FO0637 | 36 | 0.999 | N_{|\not D|}(\lambda) \underset{\lambda \rightarrow \infty}{\sim} \frac{2^{d} \operatorname{Vol}\left(\mathbb{S}^{d-1}\right)}{d(2 \pi)^{d}} \operatorname{Vol}(M) \lambda^{d} | | |
| cardona-qft-methods_FO0638 | 36 | 0.600 | \operatorname{Vol}(\mathrm{M})=\int_{\mathrm{M}} \mathrm{dvol} | | |
| cardona-qft-methods_FO0639 | 36 | 1.000 | S_{g} | | |
| cardona-qft-methods_FO0640 | 36 | 1.000 | \mathcal{H}_{g} | | |
| cardona-qft-methods_FO0641 | 36 | 1.000 | M_{g} | | |
| cardona-qft-methods_FO0642 | 36 | 1.000 | \mathcal{H}_{g}:=L^{2}\left(M_{g}, S_{g}\right) | | |
| cardona-qft-methods_FO0643 | 36 | 1.000 | g^{\prime} | | |
| cardona-qft-methods_FO0644 | 36 | 1.000 | f_{g, g^{\prime}}: M \rightarrow \mathbb{R}^{+} | | |
| cardona-qft-methods_FO0645 | 36 | 0.945 | d v o l_{g^{\prime}}=f_{g^{\prime}, g} | | |
| cardona-qft-methods_FO0646 | 36 | 1.000 | I_{g, g^{\prime}}(x): S_{g} \rightarrow S_{g^{\prime}} | | |
| cardona-qft-methods_FO0647 | 36 | 1.000 | \left|I_{g, g^{\prime}}(x) \psi(x)\right|_{g^{\prime}}= | | |
| cardona-qft-methods_FO0648 | 37 | 1.000 | |\psi(x)|_{g} | | |
| cardona-qft-methods_FO0649 | 37 | 1.000 | H_{g, g^{\prime}} | | |
| cardona-qft-methods_FO0650 | 37 | 1.000 | 2^{\lfloor d / 2\rfloor} | | |
| cardona-qft-methods_FO0651 | 37 | 1.000 | g^{\prime}(X, Y)=g\left(H_{g, g^{\prime}} X, Y\right) | | |
| cardona-qft-methods_FO0652 | 37 | 1.000 | X, Y \in T M | | |
| cardona-qft-methods_FO0653 | 37 | 1.000 | \iota_{g, g^{\prime}} X=H_{g, g^{\prime}}^{-1 / 2} X | | |
| cardona-qft-methods_FO0654 | 37 | 1.000 | \iota_{g, g^{\prime}} | | |
| cardona-qft-methods_FO0655 | 37 | 1.000 | O_{d} | | |
| cardona-qft-methods_FO0656 | 37 | 0.637 | _{d} | | |
| cardona-qft-methods_FO0657 | 37 | 0.963 | I_{g, g^{\prime}}\left(\right. | | |
| cardona-qft-methods_FO0658 | 37 | 0.963 | \left.^{6}\right) | | |
| cardona-qft-methods_FO0659 | 37 | 1.000 | I_{g, g^{\prime}}: \mathcal{H}_{g} \rightarrow \mathcal{H}_{g^{\prime}} | | |
| cardona-qft-methods_FO0660 | 37 | 0.999 | \left(I_{g, g^{\prime}} \psi\right)(x):=I_{g, g^{\prime}}(x) \psi(x) | | |
| cardona-qft-methods_FO0661 | 37 | 1.000 | U_{g^{\prime}, g} | | |
| cardona-qft-methods_FO0662 | 37 | 1.000 | \mathcal{H}_{g^{\prime}} | | |
| cardona-qft-methods_FO0663 | 37 | 1.000 | \psi^{\prime} \in \mathcal{H}_{g^{\prime}} | | |
| cardona-qft-methods_FO0664 | 37 | 1.000 | \not D_{g^{\prime}} | | |
| cardona-qft-methods_FO0665 | 37 | 1.000 | D_{g^{\prime}} | | |
| cardona-qft-methods_FO0666 | 37 | 1.000 | H^{k}\left(M_{g}, S_{g}\right) | | |
| cardona-qft-methods_FO0667 | 37 | 1.000 | \Gamma^{\infty}\left(M_{g}, S_{g}\right) | | |
| cardona-qft-methods_FO0668 | 37 | 1.000 | \|\psi\|_{k}^{2}= | | |
| cardona-qft-methods_FO0669 | 37 | 0.922 | \sum_{j=0}^{k} \int_{M}\left|\nabla^{j} \psi(x)\right|^{2} d x | | |
| cardona-qft-methods_FO0670 | 37 | 0.922 | \nabla \psi | | |
| cardona-qft-methods_FO0671 | 37 | 1.000 | T^{*} M_{g} \otimes S_{g} | | |
| cardona-qft-methods_FO0672 | 37 | 1.000 | U_{g, g^{\prime}}: H^{k}\left(M_{g}, S_{g}\right) \rightarrow H^{k}\left(M_{g^{\prime}}, S_{g^{\prime}}\right) | | |
| cardona-qft-methods_FO0673 | 37 | 0.801 | { }^{2,6,46,56} | | |
| cardona-qft-methods_FO0674 | 37 | 1.000 | g^{\prime}=e^{2 h} g | | |
| cardona-qft-methods_FO0675 | 37 | 1.000 | h \in C^{\infty}(M, \mathbb{R}) | | |
| cardona-qft-methods_FO0676 | 37 | 1.000 | I_{g, g^{\prime}} | | |
| cardona-qft-methods_FO0677 | 37 | 1.000 | S_{g^{\prime}} | | |
| cardona-qft-methods_FO0678 | 37 | 1.000 | \psi \in | | |
| cardona-qft-methods_FO0679 | 37 | 0.987 | \Gamma^{\infty}\left(M, S_{g}\right) | | |
| cardona-qft-methods_FO0680 | 38 | 1.000 | \sigma^{D_{g^{\prime}}}(x, \xi)=e^{-h(x)} c_{g}(\xi) | | |
| cardona-qft-methods_FO0681 | 38 | 0.965 | \not D_{g} | | |
| cardona-qft-methods_FO0682 | 38 | 1.000 | c_{g^{\prime}}(\xi)=e^{-h(x)} U_{g^{\prime}, g}^{-1}(x) c_{g}(\xi) U_{g^{\prime}, g}(x), \xi \in T_{x}^{*} M | | |
| cardona-qft-methods_FO0683 | 38 | 1.000 | g^{\prime}(\xi, \eta)=e^{-2 h} g(\xi, \eta) | | |
| cardona-qft-methods_FO0684 | 38 | 1.000 | c_{g}(\xi) c_{g}(\eta)+c_{g}(\eta) c_{g}(\xi)= | | |
| cardona-qft-methods_FO0685 | 38 | 0.947 | 2 g(\xi, \eta) \mathrm{id}_{S_{g}} | | |
| cardona-qft-methods_FO0686 | 38 | 1.000 | \tilde{\alpha}=H_{\alpha^{*} g, g}^{-1 / 2} T \alpha | | |
| cardona-qft-methods_FO0687 | 38 | 0.999 | g^{\prime}=\alpha^{*} g | | |
| cardona-qft-methods_FO0688 | 38 | 0.999 | \left(\alpha^{*} g\right)_{x}(\xi, \eta)= | | |
| cardona-qft-methods_FO0689 | 38 | 0.997 | g_{\alpha(x)}\left(\alpha_{*}(\xi), \alpha_{*} \eta\right), x \in M | | |
| cardona-qft-methods_FO0690 | 38 | 0.997 | \alpha_{*} | | |
| cardona-qft-methods_FO0691 | 38 | 0.997 | T_{x} M \rightarrow | | |
| cardona-qft-methods_FO0692 | 38 | 0.998 | T_{\alpha(x)} M | | |
| cardona-qft-methods_FO0693 | 38 | 1.000 | d_{g^{\prime}}=\alpha^{*} d_{g} | | |
| cardona-qft-methods_FO0694 | 38 | 1.000 | \sigma_{d}^{D}(x, \xi)=c_{g}(\xi) | | |
| cardona-qft-methods_FO0695 | 38 | 1.000 | d_{\alpha^{*} g} | | |
| cardona-qft-methods_FO0696 | 38 | 1.000 | d_{g} | | |
| cardona-qft-methods_FO0697 | 38 | 1.000 | { }^{4,43,44} | | |
| cardona-qft-methods_FO0698 | 38 | 1.000 | e^{t \Delta} | | |
| cardona-qft-methods_FO0699 | 38 | 1.000 | -\Delta | | |
| cardona-qft-methods_FO0700 | 38 | 1.000 | \lim _{t \downarrow 0} k_{t}(x, y)=\delta(x-y) | | |
| cardona-qft-methods_FO0701 | 38 | 1.000 | k_{t}(x, y)= | | |
| cardona-qft-methods_FO0702 | 38 | 1.000 | \frac{1}{2 \pi} \int_{-\infty}^{\infty} e^{-t s^{2}} e^{i s(x-y)} d s | | |
| cardona-qft-methods_FO0703 | 38 | 1.000 | d=1 | | |
| cardona-qft-methods_FO0704 | 39 | 1.000 | f \in \mathcal{D}\left(\mathbb{R}^{d}\right) | | |
| cardona-qft-methods_FO0705 | 39 | 1.000 | \lim _{t \downarrow 0} \int_{\mathbf{R}^{d}} k_{t}(x, y) f(y) d y=f(x) | | |
| cardona-qft-methods_FO0706 | 39 | 1.000 | \lambda_{n} | | |
| cardona-qft-methods_FO0707 | 39 | 1.000 | \psi_{n} \in L^{2}(U) | | |
| cardona-qft-methods_FO0708 | 39 | 1.000 | \Delta^{-1} | | |
| cardona-qft-methods_FO0709 | 39 | 1.000 | 0 \leq \lambda_{1} \leq \lambda_{2} \leq \lambda_{3} \leq | | |
| cardona-qft-methods_FO0710 | 39 | 1.000 | \cdots, \lambda_{n} \rightarrow \infty | | |
| cardona-qft-methods_FO0711 | 39 | 1.000 | f(x)=\int_{0}^{\infty} d t e^{-t x} \phi(x) | | |
| cardona-qft-methods_FO0712 | 39 | 1.000 | \operatorname{Tr}(f(-\Delta))=\int_{0}^{\infty} d t \phi(t) \operatorname{Tr}\left(e^{t \Delta}\right) | | |
| cardona-qft-methods_FO0713 | 39 | 0.986 | \operatorname{Tr}\left(e^{t \Delta}\right)=\int_{M} d v o l(x) \operatorname{tr}_{V_{x}} k_{t}(x, x) | | |
| cardona-qft-methods_FO0714 | 39 | 1.000 | \operatorname{Tr}\left(e^{t \Delta}\right)=\sum_{n=1}^{\infty} e^{t \lambda_{n}} | | |
| cardona-qft-methods_FO0715 | 39 | 1.000 | k_{t} | | |
| cardona-qft-methods_FO0716 | 39 | 1.000 | t=0 | | |
| cardona-qft-methods_FO0717 | 39 | 1.000 | P \in \Psi D O^{m}(M, V) | | |
| cardona-qft-methods_FO0718 | 39 | 1.000 | m>0 | | |
| cardona-qft-methods_FO0719 | 39 | 1.000 | k_{t}(x, y) | | |
| cardona-qft-methods_FO0720 | 39 | 1.000 | e^{-t P} | | |
| cardona-qft-methods_FO0721 | 39 | 1.000 | \left|k_{t}(x, x)-\sum_{k \leq k(n)} a_{k}(x) t^{(-d+k) / m}\right|_{\infty, n}<c_{n} t^{n} | | |
| cardona-qft-methods_FO0722 | 39 | 1.000 | 0< | | |
| cardona-qft-methods_FO0723 | 39 | 1.000 | t<1 | | |
| cardona-qft-methods_FO0724 | 39 | 1.000 | |f|_{\infty, n}:=\sup _{x \in M} \sum_{|\alpha| \leq n}\left|\partial_{x}^{\alpha} f\right| | | |
| cardona-qft-methods_FO0725 | 39 | 0.665 | (t, x, y) | | |
| cardona-qft-methods_FO0726 | 39 | 1.000 | k(t, f, P)=\operatorname{Tr}\left(f e^{-t P}\right) | | |
| cardona-qft-methods_FO0727 | 40 | 1.000 | a_{k} | | |
| cardona-qft-methods_FO0728 | 40 | 1.000 | { }^{43,44} | | |
| cardona-qft-methods_FO0729 | 40 | 1.000 | a_{2 k}(f, P) | | |
| cardona-qft-methods_FO0730 | 40 | 1.000 | a_{2 k+1}(f, P)=0 | | |
| cardona-qft-methods_FO0731 | 40 | 1.000 | \left(g^{\mu \nu}\right)_{1 \leq \mu, \nu \leq d} | | |
| cardona-qft-methods_FO0732 | 40 | 1.000 | \mathbb{A}^{\mu} | | |
| cardona-qft-methods_FO0733 | 40 | 1.000 | \mathbb{B} | | |
| cardona-qft-methods_FO0734 | 40 | 1.000 | L(V) | | |
| cardona-qft-methods_FO0735 | 40 | 1.000 | X, Y | | |
| cardona-qft-methods_FO0736 | 40 | 1.000 | \nabla^{L C} | | |
| cardona-qft-methods_FO0737 | 40 | 1.000 | \Gamma_{\mu \nu}^{\rho} | | |
| cardona-qft-methods_FO0738 | 40 | 0.993 | \nabla=d x^{\mu} \otimes\left(\partial_{\mu}+\omega_{\mu}\right) | | |
| cardona-qft-methods_FO0739 | 40 | 0.993 | g^{\mu \nu}, \mathbb{A}^{\mu} | | |
| cardona-qft-methods_FO0740 | 40 | 0.969 | a_{k}(f, P)=\int_{M} | | |
| cardona-qft-methods_FO0741 | 40 | 0.969 | _{g} \operatorname{tr}_{E}\left(f(x) a_{k}(P)(x)\right) | | |
| cardona-qft-methods_FO0742 | 40 | 1.000 | a_{k}(P)=c_{i} \alpha_{k}^{i}(P) | | |
| cardona-qft-methods_FO0743 | 40 | 1.000 | c_{i} | | |
| cardona-qft-methods_FO0744 | 40 | 1.000 | \alpha_{k}^{i}(P) | | |
| cardona-qft-methods_FO0745 | 40 | 1.000 | E, \Omega, R | | |
| cardona-qft-methods_FO0746 | 40 | 1.000 | k=2, E | | |
| cardona-qft-methods_FO0747 | 41 | 1.000 | a_{6} | | |
| cardona-qft-methods_FO0748 | 41 | 1.000 | a_{8} | | |
| cardona-qft-methods_FO0749 | 41 | 1.000 | a_{10} | | |
| cardona-qft-methods_FO0750 | 41 | 1.000 | a_{k}(P)(x)=\frac{1}{m} c_{P^{(k-d) / m}}(x) | | |
| cardona-qft-methods_FO0751 | 41 | 1.000 | k=0 | | |
| cardona-qft-methods_FO0752 | 41 | 1.000 | P \leftrightarrow P^{-1} | | |
| cardona-qft-methods_FO0753 | 41 | 1.000 | k \in \mathbb{N} | | |
| cardona-qft-methods_FO0754 | 41 | 1.000 | \mathcal{H}=L^{2}(M, S) | | |
| cardona-qft-methods_FO0755 | 41 | 1.000 | e^{-t D^{2}} | | |
| cardona-qft-methods_FO0756 | 41 | 0.994 | t>0, e^{-t D^{2}} \in \mathcal{L}^{1} | | |
| cardona-qft-methods_FO0757 | 41 | 0.994 | e^{-t D^{2}}=\left(1+D^{2}\right)^{(d+1) / 2} e^{-t D^{2}}(1+ | | |
| cardona-qft-methods_FO0758 | 41 | 1.000 | \left.D^{2}\right)^{-(d+1) / 2} | | |
| cardona-qft-methods_FO0759 | 41 | 1.000 | \left(1+D^{2}\right)^{-(d+1) / 2} \in \mathcal{L}^{1} | | |
| cardona-qft-methods_FO0760 | 41 | 1.000 | \lambda \rightarrow\left(1+\lambda^{2}\right)^{(d+1) / 2} e^{-t \lambda^{2}} | | |
| cardona-qft-methods_FO0761 | 41 | 1.000 | \operatorname{Tr}\left(e^{-t D^{2}}\right)=\sum_{n} e^{-t \lambda_{n}^{2}}<\infty | | |
| cardona-qft-methods_FO0762 | 41 | 0.989 | \left({ }^{70}\right) | | |
| cardona-qft-methods_FO0763 | 41 | 0.989 | k_{t}(x, y) \underset{t \downarrow 0^{+}}{\sim} | | |
| cardona-qft-methods_FO0764 | 41 | 1.000 | \frac{1}{(4 \pi t)^{d / 2}} \sqrt{\operatorname{det} g_{x}} \sum_{j \geq 0} k_{j}(x, y) t^{j} e^{-d_{g}(x, y)^{2} / 4 t} | | |
| cardona-qft-methods_FO0765 | 41 | 1.000 | k_{j} | | |
| cardona-qft-methods_FO0766 | 41 | 1.000 | E^{*} \otimes E | | |
| cardona-qft-methods_FO0767 | 41 | 1.000 | a_{2 j}\left(D^{2}\right)=\frac{1}{(4 \pi)^{d / 2}} \int_{M} \operatorname{tr}\left(k_{j}(x, x)\right) \sqrt{\operatorname{det} g_{x}}|d x|, \quad a_{2 j+1}\left(D^{2}\right)=0 | | |
| cardona-qft-methods_FO0768 | 41 | 1.000 | j \in \mathbb{N} | | |
| cardona-qft-methods_FO0769 | 42 | 1.000 | p, 0 \leq p \leq d, D^{-p} \in \Psi D O^{-p}(M, E) | | |
| cardona-qft-methods_FO0770 | 42 | 0.953 | p=d, W \operatorname{Res}\left(D^{-d}\right)=\frac{2}{\Gamma(p / 2)} a_{0}\left(D^{2}\right)=\frac{2}{\Gamma(p / 2)} \frac{\operatorname{Rank}(E)}{(4 \pi)^{d / 2}} \operatorname{Vol}(\mathrm{M}) | | |
| cardona-qft-methods_FO0771 | 42 | 1.000 | \operatorname{Tr}\left(e^{-t D^{2}}\right) \underset{t \downarrow 0^{+}}{\sim} a_{0}\left(D^{2}\right) t^{-d / 2} | | |
| cardona-qft-methods_FO0772 | 42 | 1.000 | D^{-d}=\left(D^{-2}\right)^{d / 2} | | |
| cardona-qft-methods_FO0773 | 42 | 1.000 | D=\not D | | |
| cardona-qft-methods_FO0774 | 42 | 0.648 | a_{2}\left(\mathcal{D}^{2}\right) | | |
| cardona-qft-methods_FO0775 | 42 | 0.648 | (19) | | |
| cardona-qft-methods_FO0776 | 42 | 0.648 | f=1 | | |
| cardona-qft-methods_FO0777 | 42 | 0.648 | { }^{43,49} | | |
| cardona-qft-methods_FO0778 | 42 | 0.480 | W \operatorname{Res}\left(\not D^{-d+2}\right)=\frac{2}{\Gamma(d / 2-1)} a_{2}\left(\not D^{2}\right)=c \int_{M} s(x) d v o l_{g}(x) | | |
| cardona-qft-methods_FO0779 | 42 | 1.000 | D \in \Psi D O^{1}(M, E) | | |
| cardona-qft-methods_FO0780 | 42 | 1.000 | \zeta_{D}^{P}(s)=\operatorname{Tr}\left(P|D|^{-s}\right) | | |
| cardona-qft-methods_FO0781 | 42 | 0.992 | W R e s P=\operatorname{Res}_{s=0} \zeta_{D}^{P}(s)=-\int_{M} c_{P}(x)|d x| | | |
| cardona-qft-methods_FO0782 | 42 | 1.000 | { }^{24,30,33,36,49} | | |
| cardona-qft-methods_FO0783 | 42 | 0.982 | \mathcal{A}=C^{\infty}(M), \mathcal{H}=L^{2}(M, S), \not D | | |
| cardona-qft-methods_FO0784 | 42 | 1.000 | x=\left(x^{1}, \cdots, x^{d}\right) | | |
| cardona-qft-methods_FO0785 | 43 | 0.985 | K O | | |
| cardona-qft-methods_FO0786 | 43 | 0.997 | \mathcal{A}, \mathcal{H}, \mathcal{D} | | |
| cardona-qft-methods_FO0787 | 43 | 1.000 | [\mathcal{D}, \pi(a)] | | |
| cardona-qft-methods_FO0788 | 43 | 1.000 | a \in \mathcal{A} | | |
| cardona-qft-methods_FO0789 | 43 | 1.000 | \mathcal{A}:= | | |
| cardona-qft-methods_FO0790 | 43 | 0.980 | \{a \in A \mid[\mathcal{D}, \pi(a)] | | |
| cardona-qft-methods_FO0791 | 43 | 0.980 | \} | | |
| cardona-qft-methods_FO0792 | 43 | 1.000 | \pi(a) | | |
| cardona-qft-methods_FO0793 | 43 | 0.994 | \chi | | |
| cardona-qft-methods_FO0794 | 43 | 0.994 | \chi=\chi^{*},[\chi, \pi(a)]=0, \forall a \in | | |
| cardona-qft-methods_FO0795 | 43 | 1.000 | \mathcal{A}, \mathcal{D} \chi=-\chi \mathcal{D} | | |
| cardona-qft-methods_FO0796 | 43 | 1.000 | d \in \mathbb{Z} / 8 | | |
| cardona-qft-methods_FO0797 | 43 | 1.000 | J: \mathcal{H} \rightarrow \mathcal{H} | | |
| cardona-qft-methods_FO0798 | 43 | 1.000 | J \mathcal{D}=\epsilon \mathcal{D} J, J^{2}=\epsilon^{\prime}, J \chi=\epsilon^{\prime \prime} \chi J | | |
| cardona-qft-methods_FO0799 | 43 | 1.000 | \epsilon, \epsilon^{\prime}, \epsilon^{\prime \prime} | | |
| cardona-qft-methods_FO0802 | 43 | 1.000 | \pi(a)^{\circ}=J \pi\left(a^{*}\right) J^{-1} | | |
| cardona-qft-methods_FO0803 | 43 | 1.000 | \mathcal{A}^{\circ} | | |
| cardona-qft-methods_FO0804 | 43 | 1.000 | \mu_{n}\left(\mathcal{D}^{-1}\right)=\mathcal{O}\left(n^{-1 / d}\right) | | |
| cardona-qft-methods_FO0805 | 43 | 1.000 | [\mathcal{D}, \mathcal{A}] | | |
| cardona-qft-methods_FO0806 | 43 | 1.000 | \delta^{n} | | |
| cardona-qft-methods_FO0807 | 43 | 1.000 | n \in \mathbb{N} | | |
| cardona-qft-methods_FO0808 | 43 | 1.000 | \delta(T)=[|\mathcal{D}|, T] | | |
| cardona-qft-methods_FO0809 | 43 | 1.000 | \mathcal{H}^{\infty}= | | |
| cardona-qft-methods_FO0810 | 43 | 1.000 | \bigcap_{k} \mathcal{D}^{k} | | |
| cardona-qft-methods_FO0811 | 43 | 1.000 | c \in | | |
| cardona-qft-methods_FO0812 | 43 | 1.000 | Z_{d}\left(\mathcal{A}, \mathcal{A} \otimes \mathcal{A}^{\circ}\right) | | |
| cardona-qft-methods_FO0813 | 43 | 1.000 | \pi_{\mathcal{D}}(c)=\chi | | |
| cardona-qft-methods_FO0814 | 43 | 1.000 | \pi_{\mathcal{D}}\left(\left(a \otimes b^{\circ}\right) \otimes a_{1} \otimes \cdots \otimes a_{d}\right)= | | |
| cardona-qft-methods_FO0815 | 43 | 1.000 | \pi(a) \pi(b)^{\circ}\left[\mathcal{D}, \pi\left(a_{1}\right)\right] \cdots\left[\mathcal{D}, \pi\left(a_{d}\right)\right] | | |
| cardona-qft-methods_FO0816 | 44 | 1.000 | { }^{20,27,30} | | |
| cardona-qft-methods_FO0817 | 44 | 1.000 | J | | |
| cardona-qft-methods_FO0818 | 44 | 1.000 | \mathcal{A} \simeq C^{\infty}(M) | | |
| cardona-qft-methods_FO0819 | 44 | 1.000 | M=\operatorname{Sp}(\mathcal{A})=\operatorname{Sp}(A) | | |
| cardona-qft-methods_FO0820 | 44 | 1.000 | \phi_{1}, \phi_{2} | | |
| cardona-qft-methods_FO0821 | 44 | 1.000 | K | | |
| cardona-qft-methods_FO0822 | 44 | 1.000 | t \in \mathbb{R} | | |
| cardona-qft-methods_FO0823 | 44 | 1.000 | F_{t}: T \in \mathcal{B}(\mathcal{H}) \rightarrow e^{i t|\mathcal{D}|} T e^{-i t|\mathcal{D}|} | | |
| cardona-qft-methods_FO0824 | 44 | 1.000 | \alpha \in \mathbb{R} | | |
| cardona-qft-methods_FO0825 | 44 | 0.777 | O P^{0}=\left\{T \mid t \rightarrow F_{t}(T) \in C^{\infty}(\mathbb{R}, \mathcal{B}(\mathcal{H}))\right\} | | |
| cardona-qft-methods_FO0826 | 44 | 0.777 | \leq 0 | | |
| cardona-qft-methods_FO0827 | 44 | 1.000 | O P^{\alpha}=\left\{\left.T|T| \mathcal{D}\right|^{-\alpha} \in O P^{0}\right\} | | |
| cardona-qft-methods_FO0828 | 44 | 1.000 | \leq \alpha | | |
| cardona-qft-methods_FO0829 | 45 | 1.000 | \delta(T)=[|\mathcal{D}|, T], \quad \nabla(T)=\left[\mathcal{D}^{2}, T\right] | | |
| cardona-qft-methods_FO0830 | 45 | 1.000 | C^{\infty}(M)=O P^{0} \bigcap L^{\infty}(M) | | |
| cardona-qft-methods_FO0831 | 45 | 1.000 | L^{\infty}(M) | | |
| cardona-qft-methods_FO0832 | 45 | 1.000 | \mathcal{A}=C^{\infty}(M) | | |
| cardona-qft-methods_FO0833 | 45 | 1.000 | O P^{\alpha} | | |
| cardona-qft-methods_FO0834 | 45 | 0.983 | \mathcal{A} \subset O P^{0}=\bigcap_{k \geq 0} \delta^{k} \subset | | |
| cardona-qft-methods_FO0835 | 45 | 1.000 | \alpha, \beta \in \mathbb{R} | | |
| cardona-qft-methods_FO0836 | 45 | 1.000 | X=a|\mathcal{D}|[\mathcal{D}, b] \mathcal{D}^{-3} | | |
| cardona-qft-methods_FO0837 | 45 | 0.842 | [\mathcal{D}, b] | | |
| cardona-qft-methods_FO0838 | 45 | 0.842 | \mathcal{D}^{-3} | | |
| cardona-qft-methods_FO0839 | 45 | 0.842 | X \in O P^{-2} | | |
| cardona-qft-methods_FO0840 | 45 | 0.838 | \mathcal{D}(\mathcal{A}) | | |
| cardona-qft-methods_FO0841 | 45 | 1.000 | \mathcal{A}, \mathcal{A}^{\circ}, \mathcal{D} | | |
| cardona-qft-methods_FO0842 | 45 | 1.000 | O P^{-\infty} | | |
| cardona-qft-methods_FO0843 | 45 | 1.000 | N | | |
| cardona-qft-methods_FO0844 | 45 | 1.000 | \mathcal{D} \in \operatorname{Diff}^{1}(M, E) | | |
| cardona-qft-methods_FO0845 | 45 | 1.000 | \Psi\left(C^{\infty}(M)\right) \subset \Psi D O(M, E) | | |
| cardona-qft-methods_FO0846 | 45 | 1.000 | { }^{30,33,49} | | |
| cardona-qft-methods_FO0847 | 45 | 1.000 | P \in \Psi^{*}(\mathcal{A}) | | |
| cardona-qft-methods_FO0848 | 45 | 1.000 | P( | | |
| cardona-qft-methods_FO0849 | 45 | 1.000 | \mathcal{D}) | | |
| cardona-qft-methods_FO0850 | 45 | 1.000 | \Re(s) \gg 1, P|\mathcal{D}|^{-s} \in \mathcal{L}^{1}(\mathcal{H}) | | |
| cardona-qft-methods_FO0851 | 45 | 0.743 | S d | | |
| cardona-qft-methods_FO0852 | 45 | 0.743 | \zeta_{\mathcal{D}}^{P}(s) \mid P \in | | |
| cardona-qft-methods_FO0853 | 45 | 1.000 | \left.\Psi(\mathcal{A}) \cap O P^{0}\right\} | | |
| cardona-qft-methods_FO0854 | 45 | 1.000 | f P=\operatorname{Res}_{s=0} \zeta_{\mathcal{D}}^{P}(s) | | |
| cardona-qft-methods_FO0855 | 45 | 1.000 | \mathcal{D}+P, P | | |
| cardona-qft-methods_FO0856 | 45 | 0.928 | f X=0 | | |
| cardona-qft-methods_FO0857 | 45 | 1.000 | X | | |
| cardona-qft-methods_FO0858 | 46 | 1.000 | \mathcal{U}(\mathcal{A}) | | |
| cardona-qft-methods_FO0859 | 46 | 1.000 | \alpha_{u} | | |
| cardona-qft-methods_FO0860 | 46 | 1.000 | a \in \mathcal{A} \rightarrow u a u^{*} \in \mathcal{A} | | |
| cardona-qft-methods_FO0861 | 46 | 0.999 | \operatorname{Inn}(\mathcal{A}) | | |
| cardona-qft-methods_FO0862 | 46 | 0.999 | \operatorname{Aut}(\mathcal{A})= | | |
| cardona-qft-methods_FO0863 | 46 | 1.000 | \{\alpha \in \operatorname{Aut}(A) \mid \alpha(\mathcal{A}) \subset \mathcal{A}\} | | |
| cardona-qft-methods_FO0864 | 46 | 1.000 | \mathcal{A}=C^{\infty}\left(M, M_{n}(\mathbb{C})\right) \simeq C^{\infty}(M) \otimes M_{n}(\mathbb{C}) | | |
| cardona-qft-methods_FO0865 | 46 | 0.997 | \mathcal{G}=C^{\infty}(M, P S U(n)) | | |
| cardona-qft-methods_FO0866 | 46 | 1.000 | \operatorname{Aut}\left(C^{\infty}(M)\right) \simeq \operatorname{Diff}(M) | | |
| cardona-qft-methods_FO0867 | 46 | 0.998 | { }^{24,49} | | |
| cardona-qft-methods_FO0868 | 46 | 0.852 | \Omega_{\mathcal{D}}^{1}(\mathcal{A})=\operatorname{span}\{a d b \mid a, b \in \mathcal{A}\} | | |
| cardona-qft-methods_FO0869 | 46 | 0.852 | d b=[\mathcal{D}, b] | | |
| cardona-qft-methods_FO0870 | 46 | 0.998 | \mathcal{D}: \mathcal{D} \rightarrow \mathcal{D}_{A}= | | |
| cardona-qft-methods_FO0871 | 46 | 1.000 | \mathcal{D}+A | | |
| cardona-qft-methods_FO0872 | 46 | 1.000 | A=A^{*} \in \Omega_{\mathcal{D}}^{1}(\mathcal{A}) | | |
| cardona-qft-methods_FO0873 | 46 | 0.552 | \Omega_{\not p}^{1}\left(C^{\infty}(M)\right)=\left\{c(d a) \mid a \in C^{\infty}(M)\right\} | | |
| cardona-qft-methods_FO0874 | 46 | 1.000 | \mathcal{D}_{A} J=\epsilon J \mathcal{D}_{A} | | |
| cardona-qft-methods_FO0875 | 46 | 0.957 | \left(\mathcal{A}, \mathcal{H}, \mathcal{D}_{A}\right) | | |
| cardona-qft-methods_FO0876 | 46 | 0.990 | \left(\mathcal{A}, \mathcal{H}, \mathcal{D}_{\widetilde{A}}\right) | | |
| cardona-qft-methods_FO0877 | 46 | 0.967 | A \in \Omega_{\mathcal{D}}^{1} | | |
| cardona-qft-methods_FO0878 | 46 | 0.967 | \mathcal{D}_{A} | | |
| cardona-qft-methods_FO0879 | 46 | 0.967 | \mathcal{D}_{\widetilde{A}} | | |
| cardona-qft-methods_FO0880 | 46 | 1.000 | \mathcal{D} \rightarrow \mathcal{D}_{u}=u \mathcal{D} u^{*} | | |
| cardona-qft-methods_FO0881 | 46 | 1.000 | \mathcal{D}_{u}=\mathcal{D}+u\left[\mathcal{D}, u^{*}\right] | | |
| cardona-qft-methods_FO0882 | 47 | 1.000 | \mathcal{D}_{A}=0 | | |
| cardona-qft-methods_FO0883 | 47 | 1.000 | \mathcal{D} \neq 0 | | |
| cardona-qft-methods_FO0884 | 47 | 0.728 | (\mathcal{A}, \mathcal{D}, \mathcal{H}) | | |
| cardona-qft-methods_FO0885 | 47 | 0.728 | X \in \Psi(\mathcal{A}) | | |
| cardona-qft-methods_FO0886 | 47 | 0.592 | f X^{*}=\overline{f X} | | |
| cardona-qft-methods_FO0887 | 47 | 0.592 | X \in \Psi(\mathcal{A}), J X J^{-1} \in | | |
| cardona-qft-methods_FO0888 | 47 | 0.997 | \Psi(\mathcal{A}) | | |
| cardona-qft-methods_FO0889 | 47 | 0.997 | f J X J^{-1}=f X^{*}=\overline{f X} | | |
| cardona-qft-methods_FO0890 | 47 | 0.999 | A=A^{*} | | |
| cardona-qft-methods_FO0891 | 47 | 0.999 | k, l \in \mathbb{N} | | |
| cardona-qft-methods_FO0892 | 47 | 0.999 | f A^{l} \mathcal{D}^{-k}, f\left(A \mathcal{D}^{-1}\right)^{k} | | |
| cardona-qft-methods_FO0893 | 47 | 0.919 | f A^{l}|\mathcal{D}|^{-k}, f \chi A^{l}|\mathcal{D}|^{-k} | | |
| cardona-qft-methods_FO0894 | 47 | 0.919 | f A^{l} \mathcal{D}|\mathcal{D}|^{-k} | | |
| cardona-qft-methods_FO0895 | 47 | 1.000 | A+\epsilon J A J^{-1} | | |
| cardona-qft-methods_FO0896 | 47 | 1.000 | A \in \Omega_{\mathcal{D}}^{1}(\mathcal{A}) | | |
| cardona-qft-methods_FO0897 | 47 | 0.982 | \zeta_{D_{\widetilde{A}}}(0)=\zeta_{D}(0)+\sum_{q=1}^{d} \frac{(-1)^{q}}{q} f\left(\widetilde{A} D^{-1}\right)^{q} | | |
| cardona-qft-methods_FO0898 | 47 | 0.942 | \nabla(T)=\left[\mathcal{D}^{2}, T\right] | | |
| cardona-qft-methods_FO0899 | 47 | 1.000 | \sigma_{z} | | |
| cardona-qft-methods_FO0900 | 47 | 1.000 | T \in O P^{q} | | |
| cardona-qft-methods_FO0901 | 47 | 1.000 | g(z, r)=\frac{1}{r!}\left(\frac{z}{2}\right) \cdots\left(\frac{z}{2}-(r-1)\right)=\binom{z / 2}{r} | | |
| cardona-qft-methods_FO0902 | 47 | 1.000 | g(z, 0)= | | |
| cardona-qft-methods_FO0903 | 48 | 1.000 | P_{A} | | |
| cardona-qft-methods_FO0904 | 48 | 1.000 | \widetilde{A} \in \mathcal{D}(\mathcal{A}) \cap O P^{0} | | |
| cardona-qft-methods_FO0905 | 48 | 1.000 | \mathcal{D}_{A} \in \mathcal{D}(\mathcal{A}) \cap O P^{1} | | |
| cardona-qft-methods_FO0906 | 48 | 1.000 | V_{A}=P_{A}-P_{0} | | |
| cardona-qft-methods_FO0907 | 48 | 1.000 | V_{A} | | |
| cardona-qft-methods_FO0908 | 48 | 1.000 | \bigcap_{k \geq 1}\left(\mathcal{D}_{A}\right)^{k} \subseteq \bigcap_{k \geq 1}|D|^{k} | | |
| cardona-qft-methods_FO0909 | 48 | 1.000 | \mathcal{D}_{A} \subseteq \bigcap_{k \geq 1}|\bar{D}|^{k} | | |
| cardona-qft-methods_FO0910 | 48 | 0.808 | \alpha, \beta \in \mathbb{R},|D|^{\beta} P_{A}|D|^{\alpha} | | |
| cardona-qft-methods_FO0911 | 48 | 1.000 | P_{A} \in O P^{-\infty} | | |
| cardona-qft-methods_FO0912 | 48 | 1.000 | X=\mathcal{D}_{A}^{2}-\mathcal{D}^{2}=\widetilde{A} \mathcal{D}+\mathcal{D} \widetilde{A}+\widetilde{A}^{2}, \quad X_{V}=X+V_{A} | | |
| cardona-qft-methods_FO0913 | 48 | 1.000 | X \in \mathcal{D}_{1}(\mathcal{A}) \cap O P^{1} | | |
| cardona-qft-methods_FO0914 | 48 | 1.000 | X_{V} \sim X \bmod O P^{-\infty} | | |
| cardona-qft-methods_FO0915 | 48 | 1.000 | Y=\log \left(D_{A}^{2}\right)-\log \left(D^{2}\right) | | |
| cardona-qft-methods_FO0916 | 48 | 1.000 | D_{A}^{2}=\mathcal{D}_{A}^{2}+P_{A} | | |
| cardona-qft-methods_FO0917 | 48 | 1.000 | X_{V} | | |
| cardona-qft-methods_FO0918 | 48 | 1.000 | Y=\log \left(D^{2}+X_{V}\right)-\log \left(D^{2}\right) | | |
| cardona-qft-methods_FO0919 | 48 | 1.000 | Y | | |
| cardona-qft-methods_FO0920 | 48 | 1.000 | O P^{-1} | | |
| cardona-qft-methods_FO0921 | 48 | 0.996 | \bmod O P^{-N-1} | | |
| cardona-qft-methods_FO0922 | 48 | 0.996 | s \in \mathbb{C} | | |
| cardona-qft-methods_FO0923 | 48 | 1.000 | K_{p}(Y, s) \in O P^{-p} | | |
| cardona-qft-methods_FO0924 | 48 | 1.000 | p \in \mathbb{N} | | |
| cardona-qft-methods_FO0925 | 48 | 1.000 | r_{1}, \cdots, r_{p} \in \mathbb{N}_{0} | | |
| cardona-qft-methods_FO0926 | 48 | 0.977 | \varepsilon^{r_{1}}(Y) \cdots \varepsilon^{r_{p}}(Y) \in \Psi(\mathcal{A}) | | |
| cardona-qft-methods_FO0927 | 48 | 1.000 | \zeta_{D_{A}}(0)-\zeta_{D}(0)=\operatorname{Tr}\left(K_{1}(Y, s)|D|^{-s}\right)_{\mid s=0} | | |
| cardona-qft-methods_FO0928 | 48 | 1.000 | \zeta_{D_{A}}(0)-\zeta_{D}(0)=-\frac{1}{2} f Y | | |
| cardona-qft-methods_FO0929 | 48 | 1.000 | f \log ((1+S)(1+T))=f \log (1+S)+ | | |
| cardona-qft-methods_FO0930 | 48 | 0.932 | f \log (1+T) | | |
| cardona-qft-methods_FO0931 | 48 | 0.932 | S, T \in \Psi(\mathcal{A}) \cap O P^{-1} | | |
| cardona-qft-methods_FO0932 | 48 | 0.932 | \log (1+S)=\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} S^{n} | | |
| cardona-qft-methods_FO0933 | 49 | 0.999 | S=D^{-1} A | | |
| cardona-qft-methods_FO0934 | 49 | 0.999 | T=A D^{-1} | | |
| cardona-qft-methods_FO0935 | 49 | 0.999 | f \log \left(1+X D^{-2}\right)=2 f \log \left(1+A D^{-1}\right) | | |
| cardona-qft-methods_FO0936 | 49 | 1.000 | -\frac{1}{2} f Y=\sum_{q=1}^{d} \frac{(-1)^{q}}{q} f\left(\widetilde{A} D^{-1}\right)^{q} | | |
| cardona-qft-methods_FO0937 | 49 | 1.000 | k \in \mathbb{N}_{0} | | |
| cardona-qft-methods_FO0938 | 49 | 0.953 | \operatorname{Res}_{s=d-k} \zeta_{D_{A}}(s)=\operatorname{Res}_{s=d-k} \zeta_{D}(s)+ | | |
| cardona-qft-methods_FO0939 | 49 | 1.000 | h(s, r, p)=(-s / 2)^{p} \int_{0 \leq t_{1} \leq \cdots \leq t_{p} \leq 1} g\left(-s t_{1}, r_{1}\right) \cdots g\left(-s t_{p}, r_{p}\right) d t | | |
| cardona-qft-methods_FO0940 | 49 | 1.000 | \left|D_{A}\right|^{k} | | |
| cardona-qft-methods_FO0941 | 49 | 1.000 | \left|D_{A}\right|^{k} \in \Psi^{k}(\mathcal{A}) | | |
| cardona-qft-methods_FO0942 | 49 | 1.000 | D_{A} | | |
| cardona-qft-methods_FO0943 | 49 | 0.718 | \operatorname{Res}_{s=0} \operatorname{Tr}\left(P\left|D_{A}\right|^{-s}\right)=f P | | |
| cardona-qft-methods_FO0944 | 49 | 0.972 | k \in \mathbb{N}_{0} f\left|D_{A}\right|^{-(d-k)}= | | |
| cardona-qft-methods_FO0945 | 49 | 0.999 | \operatorname{Res}_{s=d-k} \zeta_{D_{A}}(s) | | |
| cardona-qft-methods_FO0946 | 49 | 0.945 | \operatorname{Tad}_{\mathcal{D}+A}(k) | | |
| cardona-qft-methods_FO0947 | 49 | 0.945 | k \in | | |
| cardona-qft-methods_FO0948 | 49 | 1.000 | \{d-l: l \in \mathbb{N}\} | | |
| cardona-qft-methods_FO0949 | 49 | 1.000 | A=A^{*} \in \Omega_{\mathcal{D}}^{1} | | |
| cardona-qft-methods_FO0950 | 49 | 1.000 | \Lambda^{k} | | |
| cardona-qft-methods_FO0951 | 49 | 1.000 | \mathcal{D} \rightarrow \mathcal{D}+A | | |
| cardona-qft-methods_FO0952 | 49 | 0.655 | \mathcal{A}, \mathcal{H}, \mathcal{D}, J | | |
| cardona-qft-methods_FO0953 | 49 | 0.655 | \operatorname{Tad}_{\mathcal{D}+\tilde{A}}(k) | | |
| cardona-qft-methods_FO0954 | 49 | 1.000 | \mathcal{D} \rightarrow \mathcal{D}+\widetilde{A} | | |
| cardona-qft-methods_FO0955 | 50 | 1.000 | \operatorname{Tad}_{\mathcal{D}+\widetilde{A}}=2 \operatorname{Tad}_{\mathcal{D}+A} | | |
| cardona-qft-methods_FO0956 | 50 | 1.000 | \widetilde{A}=0 | | |
| cardona-qft-methods_FO0957 | 50 | 1.000 | \operatorname{Tad}_{D+A}(k)=0 | | |
| cardona-qft-methods_FO0958 | 50 | 1.000 | k \in \mathbb{Z}, k \leq d | | |
| cardona-qft-methods_FO0959 | 50 | 0.968 | \left(\mathrm{see}^{12}\right) | | |
| cardona-qft-methods_FO0960 | 50 | 1.000 | \alpha(b):=\mathcal{D} b \mathcal{D}^{-1} | | |
| cardona-qft-methods_FO0961 | 50 | 1.000 | A=0 | | |
| cardona-qft-methods_FO0962 | 50 | 0.999 | \left(\mathcal{A}:=C^{\infty}(M), \mathcal{H}:=L^{2}(M, S), \not D\right) | | |
| cardona-qft-methods_FO0963 | 50 | 1.000 | J a J^{-1}=a^{*}, \quad \forall a \in \mathcal{A} | | |
| cardona-qft-methods_FO0964 | 50 | 1.000 | \chi:=(-i)^{d / 2} \gamma^{1} \gamma^{2} \cdots \gamma^{d} | | |
| cardona-qft-methods_FO0965 | 50 | 0.951 | \mathcal{A}^{\circ} \simeq J \mathcal{A} J^{-1} \simeq \mathcal{A} | | |
| cardona-qft-methods_FO0966 | 50 | 0.951 | J A J^{-1}= | | |
| cardona-qft-methods_FO0967 | 50 | 0.979 | -\epsilon A^{*}, \quad \forall A \in \Omega_{\mathcal{D}}^{1}(\mathcal{A}) | | |
| cardona-qft-methods_FO0968 | 50 | 0.999 | f P | | |
| cardona-qft-methods_FO0969 | 50 | 1.000 | \log t | | |
| cardona-qft-methods_FO0970 | 50 | 1.000 | \operatorname{Tr}\left(P e^{-t \not D^{2}}\right) | | |
| cardona-qft-methods_FO0971 | 50 | 1.000 | t \rightarrow 0 | | |
| cardona-qft-methods_FO0972 | 50 | 1.000 | \zeta | | |
| cardona-qft-methods_FO0973 | 51 | 1.000 | f P=2 a_{0}^{\prime} | | |
| cardona-qft-methods_FO0974 | 51 | 1.000 | \Psi\left(C^{\infty}(M)\right) | | |
| cardona-qft-methods_FO0975 | 51 | 0.813 | f P=c | | |
| cardona-qft-methods_FO0976 | 51 | 0.813 | \operatorname{Tr}\left(P \not D^{-2 s}\right)=\frac{1}{\Gamma(s)} \int_{0}^{\infty} t^{s-1} \operatorname{Tr}\left(P e^{-t \not D^{2}}\right) d t | | |
| cardona-qft-methods_FO0977 | 51 | 1.000 | a_{k}^{\prime}, k \neq 0 | | |
| cardona-qft-methods_FO0978 | 51 | 1.000 | \operatorname{Tr}\left(P \not D^{-2 s}\right) | | |
| cardona-qft-methods_FO0979 | 51 | 1.000 | k+2 | | |
| cardona-qft-methods_FO0980 | 51 | 0.998 | \int_{0}^{1} t^{s-1} \log (t)^{k} d t=\frac{(-1)^{k} k!}{s^{k+1}} | | |
| cardona-qft-methods_FO0981 | 51 | 0.998 | \Gamma(s)=\frac{1}{s}+\gamma+s g(s) | | |
| cardona-qft-methods_FO0982 | 51 | 0.982 | \operatorname{Sp}(M) | | |
| cardona-qft-methods_FO0983 | 51 | 0.988 | \operatorname{Sp}(M)=\{d-k \mid k \in \mathbb{N}\} | | |
| cardona-qft-methods_FO0984 | 51 | 1.000 | \sigma_{d}^{\left|\mathcal{D}_{A}\right|^{-d}}=\sigma_{d}^{|\mathcal{D}|^{-d}} | | |
| cardona-qft-methods_FO0985 | 51 | 1.000 | d=4 | | |
| cardona-qft-methods_FO0986 | 51 | 1.000 | a_{4}\left(1, \mathcal{D}_{A}^{2}\right) | | |
| cardona-qft-methods_FO0987 | 51 | 1.000 | a_{k}\left(1, \mathcal{D}_{A}^{2}\right) | | |
| cardona-qft-methods_FO0988 | 51 | 1.000 | \zeta_{\mathcal{D}_{A}}(0) | | |
| cardona-qft-methods_FO0989 | 51 | 1.000 | f f(x) \not D^{-d+2}= | | |
| cardona-qft-methods_FO0990 | 51 | 1.000 | \int_{M} f(x) s(x) d v o l(x) | | |
| cardona-qft-methods_FO0991 | 51 | 1.000 | \mathcal{R}: a \in \mathcal{A} \rightarrow \mathbb{C} | | |
| cardona-qft-methods_FO0992 | 51 | 1.000 | \mathcal{R}(a)=f a \mathcal{D}^{-d+2} | | |
| cardona-qft-methods_FO0993 | 51 | 1.000 | \mathcal{R} | | |
| cardona-qft-methods_FO0994 | 51 | 0.997 | f A \mathcal{D}^{-d+1} | | |
| cardona-qft-methods_FO0995 | 51 | 0.997 | A \in \Omega_{\mathcal{D}}^{1}, \mathcal{R} | | |
| cardona-qft-methods_FO0996 | 51 | 0.932 | \left(\mathcal{A}_{i}, \mathcal{D}_{i}, \mathcal{H}_{i}\right) | | |
| cardona-qft-methods_FO0997 | 52 | 1.000 | i=1,2 | | |
| cardona-qft-methods_FO0998 | 52 | 1.000 | d_{i} | | |
| cardona-qft-methods_FO0999 | 52 | 1.000 | \chi_{1} | | |
| cardona-qft-methods_FO1000 | 52 | 1.000 | \mathcal{D}^{2}=\mathcal{D}_{1}^{2} \otimes 1+1 \otimes \mathcal{D}_{2}^{2} | | |
| cardona-qft-methods_FO1001 | 52 | 1.000 | \operatorname{Tr}\left(e^{-t \mathcal{D}_{1}^{2}}\right) \sim_{t \rightarrow 0} a_{1} t^{-d_{1} / 2} | | |
| cardona-qft-methods_FO1002 | 52 | 1.000 | \operatorname{Tr}\left(e^{-t \mathcal{D}_{2}^{2}}\right) \sim_{t \rightarrow 0} | | |
| cardona-qft-methods_FO1003 | 52 | 1.000 | a_{2} t^{-d_{2} / 2} | | |
| cardona-qft-methods_FO1004 | 52 | 0.523 | d=d_{1}+d_{2} | | |
| cardona-qft-methods_FO1005 | 52 | 1.000 | \zeta_{\mathcal{D}}(s)=\operatorname{Tr}\left(|D|^{-s}\right) | | |
| cardona-qft-methods_FO1006 | 52 | 1.000 | s=d_{1}+d_{2} | | |
| cardona-qft-methods_FO1007 | 52 | 1.000 | \zeta_{\mathcal{D}}(2 s)=\sum_{n=0}^{\infty} \mu_{n}\left(D_{1}^{2} \otimes 1+1 \otimes \mathcal{D}_{2}^{2}\right)^{-s}=\sum_{n, m=0}^{\infty}\left(\mu_{n}\left(\mathcal{D}_{1}^{2}\right)+\right. | | |
| cardona-qft-methods_FO1008 | 52 | 1.000 | \left.\mu_{m}\left(\mathcal{D}_{2}^{2}\right)\right)^{-s} | | |
| cardona-qft-methods_FO1009 | 52 | 1.000 | \left(\mu_{n}\left(\mathcal{D}_{1}\right)^{2}+\mu_{m}\left(\mathcal{D}_{2}\right)^{2}\right)^{-\left(c_{1}+c_{2}\right) / 2} \leq \mu_{n}\left(\mathcal{D}_{1}\right)^{-c_{1}} \mu_{m}\left(\mathcal{D}_{2}\right)^{-c_{2}} | | |
| cardona-qft-methods_FO1010 | 52 | 0.979 | \zeta_{\mathcal{D}}\left(c_{1}+c_{2}\right) \leq \zeta_{\mathcal{D}_{1}}\left(c_{1}\right) \zeta_{\mathcal{D}_{2}}\left(c_{2}\right) | | |
| cardona-qft-methods_FO1011 | 52 | 0.979 | c_{i}>d_{i} | | |
| cardona-qft-methods_FO1012 | 52 | 0.979 | d:=\inf \left\{c \in \mathbb{R}^{+}: \zeta_{\mathcal{D}}(c)<\infty\right\} \leq | | |
| cardona-qft-methods_FO1013 | 52 | 1.000 | d_{1}+d_{2} | | |
| cardona-qft-methods_FO1014 | 52 | 1.000 | a_{i}:= | | |
| cardona-qft-methods_FO1015 | 52 | 0.965 | \operatorname{Res}_{s=d_{i} / 2}\left(\Gamma(s) \zeta_{\mathcal{D}_{i}}(2 s)\right)=\Gamma\left(d_{i} / 2\right) \operatorname{Res}_{s=d_{i} / 2}\left(\zeta_{\mathcal{D}_{i}}(2 s)\right)=\frac{1}{2} \Gamma\left(d_{i} / 2\right) \operatorname{Res}_{s=d_{i}}\left(\zeta_{\mathcal{D}_{i}}(s)\right) | | |
| cardona-qft-methods_FO1016 | 52 | 0.946 | f(s):=\Gamma(s) \zeta_{D}(2 s), \quad f(s)=\int_{0}^{1} \operatorname{Tr}\left(e^{-t \mathcal{D}^{2}}\right) t^{s-1} d t+g(s)= | | |
| cardona-qft-methods_FO1017 | 52 | 0.999 | \int_{0}^{1} \operatorname{Tr}\left(e^{-t \mathcal{D}_{1}^{2}}\right) \operatorname{Tr}\left(e^{-t \mathcal{D}_{2}^{2}}\right) t^{s-1} d t+g(s) | | |
| cardona-qft-methods_FO1018 | 52 | 1.000 | x \in \mathbb{R} \rightarrow \int_{1}^{\infty} e^{-t x^{2}} t^{x-1} d t | | |
| cardona-qft-methods_FO1019 | 52 | 1.000 | \operatorname{Tr}\left(e^{-t \mathcal{D}_{1}^{2}}\right) \operatorname{Tr}\left(e^{-t \mathcal{D}_{2}^{2}}\right) \sim_{t \rightarrow 0} a_{1} a_{2} t^{-\left(d_{1}+d_{2}\right) / 2} | | |
| cardona-qft-methods_FO1020 | 52 | 1.000 | f(s) | | |
| cardona-qft-methods_FO1021 | 52 | 1.000 | s=\left(d_{1}+d_{2}\right) / 2 | | |
| cardona-qft-methods_FO1022 | 52 | 1.000 | \zeta_{\mathcal{D}}(s) | | |
| cardona-qft-methods_FO1023 | 52 | 0.996 | a_{i}, \frac{1}{2} \Gamma\left(\left(d_{1}+d_{2}\right) / 2\right) \operatorname{Res}_{s=d}\left(\zeta_{\mathcal{D}}(s)\right)= | | |
| cardona-qft-methods_FO1024 | 52 | 0.998 | \frac{1}{2} \Gamma\left(d_{1} / 2\right) \operatorname{Res}_{s=d_{1}}\left(\zeta_{\mathcal{D}_{1}}(s)\right) \frac{1}{2} \Gamma\left(d_{2} / 2\right) \operatorname{Res}_{s=d_{2}}\left(\zeta_{\mathcal{D}_{2}}(s)\right) | | |
| cardona-qft-methods_FO1025 | 53 | 0.936 | S_{E H}(g)=-\int_{M} s_{g}(x) d v o l_{g}(x) | | |
| cardona-qft-methods_FO1026 | 53 | 1.000 | f \not{ }^{-2} | | |
| cardona-qft-methods_FO1027 | 53 | 1.000 | \mathcal{M}_{1} | | |
| cardona-qft-methods_FO1028 | 53 | 0.992 | \int_{M} d v o l_{g}=1 | | |
| cardona-qft-methods_FO1029 | 53 | 1.000 | { }^{5} g \in \mathcal{M}_{1} | | |
| cardona-qft-methods_FO1030 | 53 | 1.000 | S_{E H}(g) | | |
| cardona-qft-methods_FO1031 | 53 | 1.000 | g: R=c g | | |
| cardona-qft-methods_FO1032 | 53 | 1.000 | s_{g}=c \operatorname{dim}(M) | | |
| cardona-qft-methods_FO1033 | 53 | 0.945 | \int_{M} f\left(s_{g}(x)\right) d v o l_{g}(x) | | |
| cardona-qft-methods_FO1034 | 53 | 1.000 | \mathcal{D}^{-1} | | |
| cardona-qft-methods_FO1035 | 53 | 1.000 | d s | | |
| cardona-qft-methods_FO1036 | 53 | 1.000 | \Omega_{\mathcal{D}}^{1}(\mathcal{A}) | | |
| cardona-qft-methods_FO1037 | 53 | 0.627 | \mathcal{D} .{ }^{10} | | |
| cardona-qft-methods_FO1038 | 53 | 0.995 | \mathcal{S}(\mathcal{D}, f, \Lambda):=\operatorname{Tr}\left(f\left(\mathcal{D}^{2} / \Lambda^{2}\right)\right) | | |
| cardona-qft-methods_FO1039 | 53 | 1.000 | f\left(\mathcal{D}^{2} / \Lambda^{2}\right) | | |
| cardona-qft-methods_FO1040 | 53 | 1.000 | \mathcal{S}(\mathcal{D}, f, \Lambda)=\operatorname{Tr}(f(\mathcal{D} / \Lambda)) | | |
| cardona-qft-methods_FO1041 | 53 | 1.000 | S(\mathcal{D}, g, \Lambda)=\operatorname{Tr}\left(f\left(\mathcal{D}^{2} / \Lambda^{2}\right)\right) | | |
| cardona-qft-methods_FO1042 | 53 | 1.000 | g(x)=f\left(x^{2}\right) | | |
| cardona-qft-methods_FO1043 | 53 | 0.939 | f(\mathcal{D} / \Lambda) | | |
| cardona-qft-methods_FO1044 | 53 | 1.000 | [-\Lambda, \Lambda] | | |
| cardona-qft-methods_FO1045 | 54 | 1.000 | \frac{1}{2}\langle J \psi, \mathcal{D} \psi\rangle | | |
| cardona-qft-methods_FO1046 | 54 | 1.000 | \psi \in \mathcal{H} | | |
| cardona-qft-methods_FO1047 | 54 | 1.000 | \langle\psi, \mathcal{D} \psi\rangle | | |
| cardona-qft-methods_FO1048 | 54 | 0.999 | \psi=\chi \psi \in \mathcal{H} | | |
| cardona-qft-methods_FO1049 | 54 | 0.999 | \mathfrak{g} | | |
| cardona-qft-methods_FO1050 | 54 | 0.999 | A \in | | |
| cardona-qft-methods_FO1051 | 54 | 1.000 | \Omega^{1}(M, \mathfrak{g}) | | |
| cardona-qft-methods_FO1052 | 54 | 1.000 | F=d a+\frac{1}{2}[A, A] \in \Omega^{2}(M, \mathfrak{g}) | | |
| cardona-qft-methods_FO1053 | 54 | 1.000 | S_{Y M}(A)=\int_{M} \operatorname{tr}(F \wedge | | |
| cardona-qft-methods_FO1054 | 54 | 0.706 | \star F) d v o l_{g} | | |
| cardona-qft-methods_FO1055 | 54 | 0.706 | G=U(1) | | |
| cardona-qft-methods_FO1056 | 54 | 1.000 | U(1) | | |
| cardona-qft-methods_FO1057 | 54 | 1.000 | \operatorname{dim}(M)=4 | | |
| cardona-qft-methods_FO1058 | 54 | 0.843 | d:^{23,24} | | |
| cardona-qft-methods_FO1059 | 54 | 1.000 | \theta=d A+A^{2} | | |
| cardona-qft-methods_FO1060 | 54 | 1.000 | I(A)=\operatorname{Tr}_{\text {Dix }}\left(\theta^{2}|\mathcal{D}|^{-d}\right) | | |
| cardona-qft-methods_FO1061 | 54 | 1.000 | P=\theta^{2}|\mathcal{D}|^{-d} | | |
| cardona-qft-methods_FO1062 | 54 | 1.000 | \operatorname{tr}\left(\sigma^{P}(x, \xi)\right)=c \operatorname{tr}(F \wedge \star F)(x) | | |
| cardona-qft-methods_FO1063 | 54 | 1.000 | d A | | |
| cardona-qft-methods_FO1064 | 54 | 1.000 | A= | | |
| cardona-qft-methods_FO1065 | 54 | 1.000 | \sum_{j} \pi\left(a_{j}\right)\left[\mathcal{D}, \pi\left(b_{j}\right)\right] | | |
| cardona-qft-methods_FO1066 | 54 | 1.000 | d A=\sum_{j}\left[\mathcal{D}, \pi\left(a_{j}\right)\right]\left[\mathcal{D}, \pi\left(b_{j}\right)\right] | | |
| cardona-qft-methods_FO1067 | 54 | 1.000 | \Omega_{\mathcal{D}}^{*}(\mathcal{A}) | | |
| cardona-qft-methods_FO1068 | 54 | 1.000 | \Omega_{\mathcal{D}}^{2} \simeq | | |
| cardona-qft-methods_FO1069 | 54 | 1.000 | \pi\left(\Omega^{2} / \pi\left(\delta\left(\operatorname{Ker}(\pi) \cap \Omega^{1}\right)\right)\right. | | |
| cardona-qft-methods_FO1070 | 54 | 1.000 | \Omega^{k}(\mathcal{A}) | | |
| cardona-qft-methods_FO1071 | 54 | 1.000 | a_{0} \delta a_{1} \cdots \delta a_{k} | | |
| cardona-qft-methods_FO1072 | 54 | 1.000 | \left.\pi\left(a_{0} \delta a_{1} \cdots \delta a_{k}\right)=a_{0}\left[\mathcal{D}, a_{1}\right] \cdots\left[\mathcal{D}, a_{k}\right]\right) | | |
| cardona-qft-methods_FO1073 | 54 | 1.000 | \mathcal{H}_{k} | | |
| cardona-qft-methods_FO1074 | 54 | 1.000 | \pi\left(\Omega^{k}(\mathcal{A})\right) | | |
| cardona-qft-methods_FO1075 | 54 | 1.000 | \left\langle A_{1}, A_{2}\right\rangle_{k}=\operatorname{Tr}_{\text {Dix }}\left(A_{2}^{*} A_{1}|\mathcal{D}|^{-d}\right) | | |
| cardona-qft-methods_FO1076 | 54 | 1.000 | A_{j} \in \pi\left(\Omega^{k}(\mathcal{A})\right) | | |
| cardona-qft-methods_FO1077 | 54 | 1.000 | \Omega^{1}(\mathcal{A}) | | |
| cardona-qft-methods_FO1078 | 54 | 1.000 | S_{Y M}(V)=\left\langle\delta V+V^{2}, \delta V+V^{2}\right\rangle | | |
| cardona-qft-methods_FO1079 | 54 | 1.000 | V \rightarrow \pi(u) V \pi\left(u^{*}\right)+\pi(u)\left[\mathcal{D}, \pi\left(u^{*}\right)\right] | | |
| cardona-qft-methods_FO1080 | 54 | 1.000 | u \in \mathcal{U}(\mathcal{A}) | | |
| cardona-qft-methods_FO1081 | 54 | 1.000 | S_{Y M}(V)=\inf \left\{I(\omega) \mid \omega \in \Omega^{1}(\mathcal{A}), \pi(\omega)=V\right\} | | |
| cardona-qft-methods_FO1082 | 55 | 1.000 | \mathcal{D}_{A}=\mathcal{D}+A | | |
| cardona-qft-methods_FO1083 | 55 | 1.000 | \operatorname{Tr}(f(\mathcal{D} / \Lambda)) \geq 0 | | |
| cardona-qft-methods_FO1084 | 55 | 1.000 | S(\mathcal{D}, f, \Lambda) | | |
| cardona-qft-methods_FO1085 | 55 | 1.000 | \zeta_{\mathcal{D}} | | |
| cardona-qft-methods_FO1086 | 55 | 1.000 | \alpha<0, \zeta_{\mathcal{D}} | | |
| cardona-qft-methods_FO1087 | 55 | 1.000 | -2 \alpha | | |
| cardona-qft-methods_FO1088 | 55 | 1.000 | a_{\alpha}=\frac{1}{2} \Gamma(-\alpha) \operatorname{Res}_{s=-2 \alpha} \zeta_{\mathcal{D}}(s) | | |
| cardona-qft-methods_FO1089 | 55 | 1.000 | \alpha=0 | | |
| cardona-qft-methods_FO1090 | 55 | 1.000 | a_{0}=\zeta_{\mathcal{D}}(0)+\operatorname{dim} \mathcal{D} | | |
| cardona-qft-methods_FO1091 | 55 | 1.000 | \alpha>0, a_{\alpha}=\zeta(-2 \alpha) \operatorname{Res}_{s=-\alpha} \Gamma(s) | | |
| cardona-qft-methods_FO1092 | 55 | 1.000 | S d^{+} | | |
| cardona-qft-methods_FO1093 | 56 | 1.000 | f_{\beta}:=\int_{0}^{\infty} f(x) x^{\beta-1} d x | | |
| cardona-qft-methods_FO1094 | 56 | 0.808 | \cdots | | |
| cardona-qft-methods_FO1095 | 56 | 0.996 | \Gamma(s / 2)|\mathcal{D}|^{-s}=\int_{0}^{\infty} e^{-t \mathcal{D}^{2}} t^{s / 2-1} d t=\int_{0}^{1} e^{-t \mathcal{D}^{2}} t^{s / 2-1} d t+ | | |
| cardona-qft-methods_FO1096 | 56 | 1.000 | x \rightarrow | | |
| cardona-qft-methods_FO1097 | 56 | 0.997 | \int_{1}^{\infty} e^{-t x^{2}} x^{s / 2-1} d t | | |
| cardona-qft-methods_FO1098 | 56 | 0.997 | \operatorname{Tr}\left(e^{-t \mathcal{D}^{2}}\right) | | |
| cardona-qft-methods_FO1099 | 56 | 1.000 | a_{\alpha} t^{\alpha} | | |
| cardona-qft-methods_FO1100 | 56 | 1.000 | a_{\alpha} \int_{0}^{1} t^{\alpha+s / 2-1} d t=\frac{2 \alpha_{a}}{s+2 \alpha} | | |
| cardona-qft-methods_FO1101 | 56 | 1.000 | \Gamma(s / 2)^{-1} \underset{s \rightarrow 0}{\sim} s / 2 | | |
| cardona-qft-methods_FO1102 | 56 | 1.000 | \int_{0}^{\infty} \operatorname{Tr}\left(e^{-t \mathcal{D}^{2}}\right) t^{s / 2-1} d t | | |
| cardona-qft-methods_FO1103 | 56 | 1.000 | \zeta_{\mathcal{D}}(0) | | |
| cardona-qft-methods_FO1104 | 56 | 1.000 | a_{0} \int_{0}^{1} t^{s / 2-1} d t=\frac{2 a_{0}}{s} | | |
| cardona-qft-methods_FO1105 | 56 | 1.000 | f(x)=g\left(x^{2}\right) | | |
| cardona-qft-methods_FO1106 | 56 | 1.000 | g(x):= | | |
| cardona-qft-methods_FO1107 | 56 | 1.000 | \int_{0}^{\infty} e^{-s x} \phi(s) d s | | |
| cardona-qft-methods_FO1108 | 56 | 1.000 | \alpha<0, s^{\alpha}=\Gamma(-\alpha)^{-1} \int_{0}^{\infty} e^{-s y} y^{-\alpha-1} d y | | |
| cardona-qft-methods_FO1109 | 56 | 1.000 | \int_{0}^{\infty} s^{\alpha} \phi(s) d s= | | |
| cardona-qft-methods_FO1110 | 56 | 1.000 | \Gamma(-\alpha)^{-1} \int_{0}^{\infty} g(y) y^{-\alpha-1} d y | | |
| cardona-qft-methods_FO1111 | 56 | 0.997 | \frac{1}{2} \int_{0}^{\infty} g(y) y^{\beta / 2-1} d y=\int_{0}^{\infty} f(x) x^{\beta-1} d x | | |
| cardona-qft-methods_FO1112 | 56 | 1.000 | \mathcal{S}(\mathcal{D}, f, \Lambda) \underset{t \downarrow 0}{\sim} \sum_{k \in\{1, \cdots, d\}} f_{k} \Lambda^{k} a_{d-k}\left(\mathcal{D}^{2}\right)+f(0) a_{d}\left(\mathcal{D}^{2}\right)+\cdots | | |
| cardona-qft-methods_FO1113 | 56 | 0.840 | f_{k}:=\frac{1}{\Gamma(k / 2)} \int_{0}^{\infty} f(s) s^{k / 2-1} d s | | |
| cardona-qft-methods_FO1114 | 56 | 1.000 | \Lambda^{0} | | |
| cardona-qft-methods_FO1115 | 56 | 1.000 | \mathcal{D} \rightarrow | | |
| cardona-qft-methods_FO1116 | 57 | 0.813 | S(\mathcal{D}, f, \Lambda) \quad \underset{\Lambda \rightarrow+\infty}{\sim} | | |
| cardona-qft-methods_FO1117 | 57 | 1.000 | \sum_{n=0}^{\infty} c_{n} \Lambda^{d-n} a_{n}\left(\mathcal{D}^{2}\right) | | |
| cardona-qft-methods_FO1118 | 57 | 1.000 | f(x)=e^{-x} | | |
| cardona-qft-methods_FO1119 | 57 | 1.000 | (-1)^{m} b_{2 m+4}\left(\mathcal{D}^{2}\right)=\frac{(4 \pi)^{2}}{m!} \mu_{m}\left(\mathcal{D}^{2}\right) | | |
| cardona-qft-methods_FO1120 | 57 | 1.000 | \mathcal{K}^{\prime}(\mathbb{R}) | | |
| cardona-qft-methods_FO1121 | 57 | 1.000 | \mathcal{K}(\mathbb{R}) | | |
| cardona-qft-methods_FO1122 | 57 | 0.981 | a \in \mathbb{R}, \phi^{(k)}(x)= | | |
| cardona-qft-methods_FO1123 | 57 | 1.000 | \mathcal{O}\left(|x|^{a-k}\right) | | |
| cardona-qft-methods_FO1124 | 57 | 1.000 | |x| \rightarrow \infty | | |
| cardona-qft-methods_FO1125 | 57 | 1.000 | g\left(\Lambda^{-1}\right) | | |
| cardona-qft-methods_FO1126 | 57 | 1.000 | M=\mathbb{T}^{d} | | |
| cardona-qft-methods_FO1127 | 57 | 1.000 | \Delta=\delta^{\mu \nu} \partial_{\mu} \partial_{\nu}, \operatorname{Tr}\left(e^{t \Delta}\right)= | | |
| cardona-qft-methods_FO1128 | 57 | 1.000 | \frac{(4 \pi)^{-d / 2} \operatorname{Vol}\left(\mathbb{T}^{\mathrm{d}}\right)}{t^{d / 2}}+\mathcal{O}\left(t^{-d / 2} e^{-1 / 4 t}\right) | | |
| cardona-qft-methods_FO1129 | 57 | 1.000 | \operatorname{Tr}\left(e^{t \Delta}\right) \simeq | | |
| cardona-qft-methods_FO1130 | 57 | 0.999 | \frac{(4 \pi)^{-d / 2} \operatorname{Vol}\left(\mathrm{~T}^{\mathrm{d}}\right)}{t^{d / 2}}, t \rightarrow 0 | | |
| cardona-qft-methods_FO1131 | 57 | 1.000 | \mathbb{S}^{4} | | |
| cardona-qft-methods_FO1132 | 58 | 0.530 | \left(\mathrm{see}^{19}\right) | | |
| cardona-qft-methods_FO1133 | 58 | 1.000 | B_{2 k} | | |
| cardona-qft-methods_FO1134 | 58 | 1.000 | t^{2} \operatorname{Tr}\left(e^{-t \not D^{2}}\right) \simeq \frac{2}{3}+\frac{2}{3} t+\sum_{k=0}^{\infty} a_{k} t^{k+2} | | |
| cardona-qft-methods_FO1135 | 58 | 1.000 | a_{k}>\frac{4}{3 k!} \frac{\left|B_{2 k+4}\right|}{2 k+4}>0 | | |
| cardona-qft-methods_FO1136 | 58 | 1.000 | \left|B_{2 k+4}\right|=2 \frac{(2 k+4)!}{(2 \pi)^{2 k+4}} \zeta(2 k+4) \simeq | | |
| cardona-qft-methods_FO1137 | 58 | 1.000 | 4 \sqrt{\pi(k+2)}\left(\frac{k+2}{\pi e}\right)^{2 k+4} \rightarrow \infty | | |
| cardona-qft-methods_FO1138 | 58 | 1.000 | k \rightarrow \infty | | |
| cardona-qft-methods_FO1139 | 58 | 1.000 | 2 k>d | | |
| cardona-qft-methods_FO1140 | 58 | 1.000 | 2 k \leq d | | |
| cardona-qft-methods_FO1141 | 58 | 1.000 | e^{-t \sqrt{-\Delta}} | | |
| cardona-qft-methods_FO1142 | 58 | 1.000 | \mathbb{T}^{1} | | |
| cardona-qft-methods_FO1143 | 58 | 1.000 | \operatorname{Vol}\left(\mathbb{T}^{1}\right)=2 \pi | | |
| cardona-qft-methods_FO1144 | 58 | 1.000 | \operatorname{Tr}\left(e^{-t \sqrt{-\Delta}}\right)=\frac{\sinh (t)}{\cosh (t)-1}=\operatorname{coth}\left(\frac{t}{2}\right)=\frac{2}{t} \sum_{k=0}^{\infty} \frac{B_{2 k}}{(2 k)!} t^{2 k}=\frac{2}{t}\left[1+\frac{t^{2}}{12}-\frac{t^{4}}{720}+\mathcal{O}\left(t^{6}\right)\right] | | |
| cardona-qft-methods_FO1145 | 58 | 0.998 | t<2 \pi | | |
| cardona-qft-methods_FO1146 | 58 | 0.998 | \frac{B_{2 k}}{(2 k)!}=(-1)^{k+1} \frac{2 \zeta(2 k)}{(2 \pi)^{2 k}} | | |
| cardona-qft-methods_FO1147 | 58 | 0.998 | \frac{\left|B_{2 k}\right|}{(2 k)!} \simeq | | |
| cardona-qft-methods_FO1148 | 58 | 1.000 | \frac{2}{(2 \pi)^{2 k}} | | |
| cardona-qft-methods_FO1149 | 58 | 1.000 | t \rightarrow \infty | | |
| cardona-qft-methods_FO1150 | 59 | 1.000 | \mathbb{T}^{d} | | |
| cardona-qft-methods_FO1151 | 59 | 1.000 | \operatorname{Tr}\left(e^{t \Delta}\right) | | |
| cardona-qft-methods_FO1152 | 59 | 1.000 | N(\lambda) | | |
| cardona-qft-methods_FO1153 | 59 | 0.999 | \lambda | | |
| cardona-qft-methods_FO1154 | 59 | 0.999 | N(\lambda)= | | |
| cardona-qft-methods_FO1155 | 59 | 0.892 | \frac{(4 \pi)^{-d / 2} \operatorname{Vol}\left(\mathbb{T}^{\mathrm{d}}\right)}{\Gamma(d / 2+1)} \lambda^{d / 2}+o\left(\lambda^{d / 2}\right) | | |
| cardona-qft-methods_FO1156 | 59 | 1.000 | t | | |
| cardona-qft-methods_FO1157 | 59 | 0.892 | \lambda .{ }^{38} | | |
| cardona-qft-methods_FO1158 | 59 | 1.000 | { }^{16,76} | | |
| cardona-qft-methods_FO1159 | 59 | 1.000 | S U_{q}(2) | | |
| cardona-qft-methods_FO1160 | 59 | 0.958 | A \in \Gamma^{\infty}(M, \operatorname{End}(S)) | | |
| cardona-qft-methods_FO1161 | 59 | 1.000 | \mathcal{D}=i \gamma^{\mu}\left(\partial_{\mu}+A_{\mu}\right) | | |
| cardona-qft-methods_FO1162 | 59 | 1.000 | F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu}+ | | |
| cardona-qft-methods_FO1163 | 59 | 1.000 | \left[A_{\mu}, A_{\nu}\right] | | |
| cardona-qft-methods_FO1164 | 59 | 1.000 | P=\mathcal{D}^{2} | | |
| cardona-qft-methods_FO1165 | 59 | 1.000 | a_{i}(1, P) | | |
| cardona-qft-methods_FO1166 | 59 | 1.000 | i=0,2,4 | | |
| cardona-qft-methods_FO1167 | 59 | 1.000 | { }^{20,30} | | |
| cardona-qft-methods_FO1168 | 59 | 1.000 | { }^{10,15,17,57,63,64,71,79} | | |
| cardona-qft-methods_FO1169 | 60 | 1.000 | S U(2) | | |
| cardona-qft-methods_FO1170 | 60 | 1.000 | \mathbb{S}^{3} \times \mathbb{S}^{1} | | |
| cardona-qft-methods_FO1171 | 60 | 1.000 | { }^{16,19} | | |
| cardona-qft-methods_FO1172 | 60 | 1.000 | { }^{66,76-78,81,95} | | |
| cardona-qft-methods_FO1173 | 60 | 1.000 | { }^{14,18,18,58,59,61} | | |
| cardona-qft-methods_FO1174 | 60 | 1.000 | { }^{53,84,85} | | |
| cardona-qft-methods_FO1175 | 60 | 1.000 | C^{\infty}\left(\mathbb{T}_{\Theta}^{n}\right) | | |
| cardona-qft-methods_FO1176 | 60 | 1.000 | n | | |
| cardona-qft-methods_FO1177 | 60 | 1.000 | \Theta \in M_{n}(\mathbb{R}) | | |
| cardona-qft-methods_FO1178 | 60 | 1.000 | \mathbb{T}^{n} | | |
| cardona-qft-methods_FO1179 | 60 | 1.000 | u_{i}, i=1, \ldots, n | | |
| cardona-qft-methods_FO1180 | 60 | 0.993 | u_{l} u_{j}=e^{i \Theta_{l j}} u_{j} u_{l} | | |
| cardona-qft-methods_FO1181 | 60 | 0.999 | a \in C^{\infty}\left(\mathbb{T}_{\Theta}^{n}\right) | | |
| cardona-qft-methods_FO1182 | 60 | 0.999 | a=\sum_{k \in \mathbb{Z}^{n}} a_{k} U_{k} | | |
| cardona-qft-methods_FO1183 | 60 | 0.999 | \left\{a_{k}\right\} \in \mathcal{S}\left(\mathbb{Z}^{n}\right) | | |
| cardona-qft-methods_FO1184 | 60 | 0.998 | U_{k}=e^{-\frac{i}{2} k \cdot \chi k} u_{1}^{k_{1}} \cdots u_{n}^{k_{n}}, k \in \mathbb{Z}^{n} | | |
| cardona-qft-methods_FO1185 | 61 | 1.000 | \Theta | | |
| cardona-qft-methods_FO1186 | 61 | 1.000 | U_{k} | | |
| cardona-qft-methods_FO1187 | 61 | 1.000 | U_{k}^{*}=U_{-k} | | |
| cardona-qft-methods_FO1188 | 61 | 1.000 | \left[U_{k}, U_{l}\right]=-2 i \sin \left(\frac{1}{2} k . \Theta l\right) U_{k+l} | | |
| cardona-qft-methods_FO1189 | 61 | 1.000 | \tau\left(\sum_{k \in \mathbb{Z}^{n}} a_{k} U_{k}\right)=a_{0} | | |
| cardona-qft-methods_FO1190 | 61 | 1.000 | \mathcal{H}_{\tau} | | |
| cardona-qft-methods_FO1191 | 61 | 1.000 | \langle a, b\rangle=\tau\left(a^{*} b\right) | | |
| cardona-qft-methods_FO1192 | 61 | 0.992 | \mathcal{H}_{\tau}=\left\{\sum_{k \in \mathbb{Z}^{n}} a_{k} U_{k} \mid\left\{a_{k}\right\}_{k} \in l^{2}\left(\mathbb{Z}^{n}\right)\right\} | | |
| cardona-qft-methods_FO1193 | 61 | 1.000 | L( | | |
| cardona-qft-methods_FO1194 | 61 | 1.000 | ) and R( | | |
| cardona-qft-methods_FO1195 | 61 | 1.000 | ) . | | |
| cardona-qft-methods_FO1196 | 61 | 1.000 | \delta_{\mu}, \mu \in\{1, \ldots, n\} | | |
| cardona-qft-methods_FO1197 | 61 | 1.000 | \delta_{\mu}\left(U_{k}\right)=i k_{\mu} U_{k} | | |
| cardona-qft-methods_FO1198 | 61 | 1.000 | \mathcal{A}_{\Theta}=C^{\infty}\left(\mathbb{T}_{\Theta}^{n}\right) | | |
| cardona-qft-methods_FO1199 | 61 | 1.000 | \mathcal{H}=\mathcal{H}_{\tau} \otimes \mathbb{C}^{2^{m}} | | |
| cardona-qft-methods_FO1200 | 61 | 1.000 | n=2 m | | |
| cardona-qft-methods_FO1201 | 61 | 1.000 | n=2 m+1 | | |
| cardona-qft-methods_FO1202 | 61 | 1.000 | m=\left\lfloor\frac{n}{2}\right\rfloor | | |
| cardona-qft-methods_FO1203 | 61 | 1.000 | \frac{n}{2} | | |
| cardona-qft-methods_FO1204 | 61 | 1.000 | \mathcal{A}_{\Theta} | | |
| cardona-qft-methods_FO1205 | 61 | 1.000 | L(a) \otimes 1_{2^{m}} | | |
| cardona-qft-methods_FO1206 | 61 | 1.000 | J_{0}(a)=a^{*} | | |
| cardona-qft-methods_FO1207 | 61 | 1.000 | \left[J_{0}, \delta_{\mu}\right]=0 | | |
| cardona-qft-methods_FO1208 | 61 | 1.000 | J=J_{0} \otimes C_{0} | | |
| cardona-qft-methods_FO1209 | 61 | 1.000 | C_{0} | | |
| cardona-qft-methods_FO1210 | 61 | 1.000 | \mathbb{C}^{2^{m}} | | |
| cardona-qft-methods_FO1211 | 61 | 1.000 | C^{\infty}\left(\mathbb{T}_{\Theta}^{n}\right) \otimes \mathbb{C}^{2^{m}} | | |
| cardona-qft-methods_FO1212 | 61 | 1.000 | C_{0} \gamma^{\alpha}=-\varepsilon \gamma^{\alpha} C_{0} | | |
| cardona-qft-methods_FO1213 | 61 | 1.000 | \mathcal{D} U_{k} \otimes e_{i}=k_{\mu} U_{k} \otimes \gamma^{\mu} e_{i} | | |
| cardona-qft-methods_FO1214 | 61 | 0.992 | \left(e_{i}\right) | | |
| cardona-qft-methods_FO1215 | 61 | 0.992 | C_{0}^{2}= \pm 1_{2^{m}} | | |
| cardona-qft-methods_FO1216 | 61 | 1.000 | \chi=i d \otimes(-i)^{m} \gamma^{1} \cdots \gamma^{n} | | |
| cardona-qft-methods_FO1217 | 61 | 0.710 | \left(\mathcal{A}_{\Theta}, \mathcal{H}, \mathcal{D}, J, \chi\right) | | |
| cardona-qft-methods_FO1218 | 61 | 1.000 | u \in \mathcal{A}, u u^{*}=u^{*} u=U_{0} | | |
| cardona-qft-methods_FO1219 | 61 | 1.000 | V_{u} \mathcal{D} V_{u}^{*} | | |
| cardona-qft-methods_FO1220 | 61 | 1.000 | V_{u}=\left(L(u) \otimes 1_{2^{m}}\right) J\left(L(u) \otimes 1_{2^{m}}\right) J^{-1} | | |
| cardona-qft-methods_FO1221 | 61 | 0.990 | J \mathcal{D}=\epsilon \mathcal{D} J | | |
| cardona-qft-methods_FO1222 | 61 | 0.552 | \mathcal{D}_{A}=\mathcal{D}+A+\epsilon J A J^{-1} | | |
| cardona-qft-methods_FO1223 | 61 | 0.552 | V_{u} \mathcal{D} V_{u}^{*}=\mathcal{D}_{L(u) \otimes 1_{2} m\left[\mathcal{D}, L\left(u^{*}\right) \otimes 1_{2} m\right]} | | |
| cardona-qft-methods_FO1224 | 61 | 1.000 | V_{u} \mathcal{D}_{A} V_{u}^{*}=\mathcal{D}_{\gamma_{u}(A)} | | |
| cardona-qft-methods_FO1225 | 61 | 1.000 | \gamma_{u}(A)=u\left[\mathcal{D}, u^{*}\right]+u A u^{*} | | |
| cardona-qft-methods_FO1226 | 61 | 1.000 | L(u) \otimes 1_{2^{m}} \longrightarrow u | | |
| cardona-qft-methods_FO1227 | 61 | 1.000 | \mathcal{S}\left(\mathcal{D}_{A}, f, \Lambda\right)=\mathcal{S}\left(\mathcal{D}_{\gamma_{u}(A)}, f, \Lambda\right) | | |
| cardona-qft-methods_FO1228 | 61 | 1.000 | A=L\left(-i A_{\alpha}\right) \otimes | | |
| cardona-qft-methods_FO1229 | 61 | 0.981 | \gamma^{\alpha}, A_{\alpha}=-A_{\alpha}^{*} \in \mathcal{A}_{\Theta} | | |
| cardona-qft-methods_FO1230 | 61 | 0.981 | \mathcal{D}_{A}=-i\left(\delta_{\alpha}+L\left(A_{\alpha}\right)-R\left(A_{\alpha}\right)\right) \otimes \gamma^{\alpha} | | |
| cardona-qft-methods_FO1231 | 62 | 1.000 | \tilde{A}_{\alpha}=L\left(A_{\alpha}\right)-R\left(A_{\alpha}\right) | | |
| cardona-qft-methods_FO1232 | 62 | 1.000 | \mathcal{D}_{A}^{2}=-g^{\alpha_{1} \alpha_{2}}\left(\delta_{\alpha_{1}}+\tilde{A}_{\alpha_{1}}\right)\left(\delta_{\alpha_{2}}+\tilde{A}_{\alpha_{2}}\right) \otimes 1_{2^{m}}-\frac{1}{2} \Omega_{\alpha_{1} \alpha_{2}} \otimes \gamma^{\alpha_{1} \alpha_{2}} | | |
| cardona-qft-methods_FO1233 | 62 | 1.000 | \mathcal{D}=U_{0} \otimes \mathbb{C}^{2^{m}} | | |
| cardona-qft-methods_FO1234 | 62 | 1.000 | \operatorname{dim} \mathcal{D}=2^{m} | | |
| cardona-qft-methods_FO1235 | 62 | 1.000 | \mathcal{D} \subseteq \mathcal{D}_{A} | | |
| cardona-qft-methods_FO1236 | 62 | 1.000 | u \in \mathcal{A}, \mathcal{D}_{\gamma_{u}(A)}=V_{u} \mathcal{D}_{A} | | |
| cardona-qft-methods_FO1237 | 62 | 1.000 | \mathcal{D}_{A}=\mathcal{D} | | |
| cardona-qft-methods_FO1238 | 62 | 1.000 | A=A_{u}=L(u) \otimes 1_{2^{m}}\left[\mathcal{D}, L\left(u^{*}\right) \otimes 1_{2^{m}}\right] | | |
| cardona-qft-methods_FO1239 | 62 | 1.000 | u | | |
| cardona-qft-methods_FO1240 | 62 | 0.995 | \|A\|<\frac{1}{2} | | |
| cardona-qft-methods_FO1241 | 62 | 1.000 | \frac{1}{2 \pi} \Theta | | |
| cardona-qft-methods_FO1242 | 62 | 1.000 | \mathcal{D}=\mathcal{D}_{A} | | |
| cardona-qft-methods_FO1243 | 62 | 1.000 | \delta>0 | | |
| cardona-qft-methods_FO1244 | 62 | 1.000 | a \in \mathbb{R}^{n} | | |
| cardona-qft-methods_FO1245 | 62 | 1.000 | \delta | | |
| cardona-qft-methods_FO1246 | 62 | 0.947 | c>0 | | |
| cardona-qft-methods_FO1247 | 62 | 0.947 | |q \cdot a-m| \geq c|q|^{-\delta}, \forall q \in \mathbb{Z}^{n} \backslash\{0\} | | |
| cardona-qft-methods_FO1248 | 62 | 1.000 | \forall m \in \mathbb{Z} | | |
| cardona-qft-methods_FO1249 | 62 | 0.996 | \mathcal{B} \mathcal{V}(\delta) | | |
| cardona-qft-methods_FO1250 | 62 | 0.996 | \mathcal{B} \mathcal{V}:= | | |
| cardona-qft-methods_FO1251 | 62 | 1.000 | \cup_{\delta>0} \mathcal{B} \mathcal{V}(\delta) | | |
| cardona-qft-methods_FO1252 | 62 | 1.000 | \Theta \in \mathcal{M}_{n}(\mathbb{R}) | | |
| cardona-qft-methods_FO1253 | 62 | 1.000 | n \times n | | |
| cardona-qft-methods_FO1254 | 62 | 1.000 | u \in \mathbb{Z}^{n} | | |
| cardona-qft-methods_FO1255 | 62 | 1.000 | { }^{t} \Theta(u) | | |
| cardona-qft-methods_FO1256 | 62 | 1.000 | \mathbb{R}^{n} | | |
| cardona-qft-methods_FO1257 | 62 | 1.000 | \delta>n | | |
| cardona-qft-methods_FO1258 | 62 | 0.975 | \mathbb{R}^{n} \backslash \mathcal{B V}(\delta) | | |
| cardona-qft-methods_FO1259 | 62 | 1.000 | i | | |
| cardona-qft-methods_FO1260 | 62 | 0.666 | L_{i} \in \mathcal{B} \mathcal{V} | | |
| cardona-qft-methods_FO1261 | 62 | 0.666 | { }^{t} \Theta\left(e_{i}\right) \in \mathcal{B} \mathcal{V} | | |
| cardona-qft-methods_FO1262 | 62 | 1.000 | \mathcal{M}_{n}(\mathbb{R}) \approx \mathbb{R}^{n^{2}} | | |
| cardona-qft-methods_FO1263 | 63 | 1.000 | \left(C^{\infty}\left(\mathbb{T}_{\Theta}^{n}\right), \mathcal{H}, \mathcal{D}\right) | | |
| cardona-qft-methods_FO1264 | 63 | 1.000 | \left\{n-k: k \in \mathbb{N}_{0}\right\} | | |
| cardona-qft-methods_FO1265 | 63 | 1.000 | \zeta_{D}(0)=0 | | |
| cardona-qft-methods_FO1266 | 63 | 1.000 | \zeta_{D}(0) | | |
| cardona-qft-methods_FO1267 | 63 | 1.000 | \zeta_{D_{A}}(0) | | |
| cardona-qft-methods_FO1268 | 63 | 0.813 | C^{\infty}\left(\mathbb{T}_{\Theta}^{n}\right), \mathcal{H}, \mathcal{D} | | |
| cardona-qft-methods_FO1269 | 63 | 1.000 | A=L\left(-i A_{\alpha}\right) \otimes \gamma^{\alpha} | | |
| cardona-qft-methods_FO1270 | 63 | 1.000 | n=2, \mathcal{S}\left(\mathcal{D}_{A}, f, \Lambda\right)=4 \pi f_{2} \Lambda^{2}+\mathcal{O}\left(\Lambda^{-2}\right) | | |
| cardona-qft-methods_FO1271 | 63 | 1.000 | n=4, \mathcal{S}\left(\mathcal{D}_{A}, f, \Lambda\right)=8 \pi^{2} f_{4} \Lambda^{4}-\frac{4 \pi^{2}}{3} f(0) \tau\left(F_{\mu \nu} F^{\mu \nu}\right)+\mathcal{O}\left(\Lambda^{-2}\right) | | |
| cardona-qft-methods_FO1272 | 63 | 1.000 | \mathcal{S}\left(\mathcal{D}_{A}, f, \Lambda\right)=\sum_{k=0}^{n} f_{n-k} c_{n-k}(A) \Lambda^{n-k}+ | | |
| cardona-qft-methods_FO1273 | 63 | 1.000 | \mathcal{O}\left(\Lambda^{-1}\right), c_{n-2}(A)=0, c_{n-k}(A)=0 | | |
| cardona-qft-methods_FO1274 | 63 | 1.000 | c_{0}(A)=0 | | |
| cardona-qft-methods_FO1275 | 63 | 1.000 | n=4 | | |
| cardona-qft-methods_FO1276 | 63 | 1.000 | A_{\alpha} \longrightarrow \gamma_{u}\left(A_{\alpha}\right)=u A_{\alpha} u^{*}+u \delta_{\alpha}\left(u^{*}\right) | | |
| cardona-qft-methods_FO1277 | 63 | 1.000 | u=U_{k} | | |
| cardona-qft-methods_FO1278 | 63 | 1.000 | U_{k} \delta_{\alpha}\left(U_{k}^{*}\right)=-i k_{\alpha} U_{0} | | |
| cardona-qft-methods_FO1279 | 64 | 1.000 | A, \mathcal{D}_{A}=\mathcal{D} | | |
| cardona-qft-methods_FO1280 | 64 | 1.000 | \Theta=\theta\left(\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right) | | |
| cardona-qft-methods_FO1281 | 64 | 1.000 | \theta \in \mathbb{R} | | |
| cardona-qft-methods_FO1282 | 64 | 1.000 | H\left(\mathcal{A}_{\Theta}, \mathcal{A}_{\Theta}{ }^{*}\right) | | |
| cardona-qft-methods_FO1283 | 64 | 0.996 | \operatorname{dim} H^{j}\left(\mathcal{A}_{\Theta}, \mathcal{A}_{\Theta}{ }^{*}\right)=2 | | |
| cardona-qft-methods_FO1284 | 64 | 0.996 | j=1 | | |
| cardona-qft-methods_FO1285 | 64 | 0.996 | j=2 | | |
| cardona-qft-methods_FO1286 | 64 | 1.000 | \theta | | |
| cardona-qft-methods_FO1287 | 64 | 1.000 | \left|1-e^{i 2 \pi n \theta}\right|^{-1}= | | |
| cardona-qft-methods_FO1288 | 64 | 1.000 | \mathcal{O}\left(n^{k}\right) | | |
| cardona-qft-methods_FO1289 | 64 | 1.000 | \mathbb{Z}^{n} | | |
| cardona-qft-methods_FO1291 | 71 | 0.998 | { }^{3-5,13,17} | | |
| cardona-qft-methods_FO1292 | 71 | 0.997 | { }^{11,25} | | |
| cardona-qft-methods_FO1293 | 72 | 1.000 | A: \mathcal{H}_{1} \rightarrow \mathcal{H}_{2} | | |
| cardona-qft-methods_FO1294 | 72 | 0.997 | \mathcal{H}_{1} | | |
| cardona-qft-methods_FO1295 | 72 | 0.997 | \mathcal{H}_{2} | | |
| cardona-qft-methods_FO1296 | 72 | 0.840 | \operatorname{Coker}(A):=\mathcal{H}_{2} / \operatorname{Im}(A) | | |
| cardona-qft-methods_FO1297 | 72 | 0.840 | \operatorname{dim} \operatorname{Ker}(A) | | |
| cardona-qft-methods_FO1298 | 72 | 0.974 | \operatorname{dim} \operatorname{Coker}(A) | | |
| cardona-qft-methods_FO1299 | 72 | 0.999 | \operatorname{Ker}(A) | | |
| cardona-qft-methods_FO1300 | 72 | 0.999 | \operatorname{Coker}(A) | | |
| cardona-qft-methods_FO1301 | 72 | 0.994 | \operatorname{Im}(A) | | |
| cardona-qft-methods_FO1302 | 72 | 0.985 | \mathcal{H}_{1}, \mathcal{H}_{2} | | |
| cardona-qft-methods_FO1303 | 72 | 0.506 | \operatorname{dim} \operatorname{Ker}(A)<\infty, \operatorname{dim} \operatorname{Coker}(A)<\infty | | |
| cardona-qft-methods_FO1304 | 72 | 1.000 | \operatorname{Ind}(A) | | |
| cardona-qft-methods_FO1305 | 72 | 1.000 | { }^{20 \mathrm{a}} | | |
| cardona-qft-methods_FO1306 | 72 | 1.000 | A(t) | | |
| cardona-qft-methods_FO1307 | 72 | 1.000 | \operatorname{Ind}(A(t)) | | |
| cardona-qft-methods_FO1308 | 72 | 1.000 | \operatorname{Ind}(A+K)=\operatorname{Ind}(A) | | |
| cardona-qft-methods_FO1309 | 72 | 0.992 | { }^{\mathrm{a}} | | |
| cardona-qft-methods_FO1310 | 72 | 1.000 | { }^{21,22} | | |
| cardona-qft-methods_FO1311 | 73 | 1.000 | T: \mathcal{H} \rightarrow \mathcal{H} | | |
| cardona-qft-methods_FO1312 | 73 | 1.000 | \operatorname{dim} \operatorname{Ker}(T)=2 | | |
| cardona-qft-methods_FO1313 | 73 | 1.000 | \operatorname{Coker}(T)=\{0\} | | |
| cardona-qft-methods_FO1314 | 73 | 1.000 | \operatorname{Ind}(T)=2 | | |
| cardona-qft-methods_FO1315 | 73 | 0.999 | \operatorname{Ind}(A)=0 | | |
| cardona-qft-methods_FO1316 | 73 | 0.999 | A: \mathcal{H} \rightarrow \mathcal{H} | | |
| cardona-qft-methods_FO1317 | 73 | 1.000 | \operatorname{dim} \mathcal{H}=\infty | | |
| cardona-qft-methods_FO1318 | 73 | 1.000 | B: \mathcal{H}_{2} \rightarrow \mathcal{H}_{3} | | |
| cardona-qft-methods_FO1319 | 73 | 1.000 | B A: \mathcal{H}_{1} \rightarrow \mathcal{H}_{3} | | |
| cardona-qft-methods_FO1320 | 73 | 0.983 | A^{*}: \mathcal{H}_{2} \rightarrow \mathcal{H}_{1} | | |
| cardona-qft-methods_FO1321 | 73 | 0.991 | \operatorname{Ind}(A)>0 | | |
| cardona-qft-methods_FO1322 | 73 | 0.991 | \operatorname{Ker}(A) \neq\{0\} | | |
| cardona-qft-methods_FO1323 | 73 | 1.000 | A x=0 | | |
| cardona-qft-methods_FO1324 | 73 | 1.000 | \operatorname{Ind}(A+K)=\operatorname{Ind}(K)>0 | | |
| cardona-qft-methods_FO1325 | 73 | 1.000 | B | | |
| cardona-qft-methods_FO1326 | 73 | 1.000 | B=A+K | | |
| cardona-qft-methods_FO1327 | 74 | 1.000 | \operatorname{Fred}\left(\mathcal{H}_{1}, \mathcal{H}_{2}\right) | | |
| cardona-qft-methods_FO1328 | 74 | 1.000 | d(A, B):=\|A-B\| | | |
| cardona-qft-methods_FO1329 | 74 | 1.000 | \operatorname{Ind}(A)=\operatorname{Ind}(B) | | |
| cardona-qft-methods_FO1330 | 74 | 1.000 | \operatorname{Irr}(G) | | |
| cardona-qft-methods_FO1331 | 74 | 1.000 | m_{V} V | | |
| cardona-qft-methods_FO1332 | 74 | 1.000 | V \oplus V \oplus \cdots \oplus V | | |
| cardona-qft-methods_FO1333 | 74 | 1.000 | m_{V} | | |
| cardona-qft-methods_FO1334 | 74 | 1.000 | m_{V} \in \mathbb{N} | | |
| cardona-qft-methods_FO1335 | 74 | 1.000 | x \in \operatorname{Ker}(A), g \in G | | |
| cardona-qft-methods_FO1336 | 74 | 1.000 | g x \in \operatorname{Ker}(A) | | |
| cardona-qft-methods_FO1337 | 75 | 1.000 | m_{+}, m_{-} | | |
| cardona-qft-methods_FO1338 | 75 | 0.886 | R(G) | | |
| cardona-qft-methods_FO1339 | 75 | 0.886 | V-U | | |
| cardona-qft-methods_FO1340 | 75 | 1.000 | V_{1}-V_{2} | | |
| cardona-qft-methods_FO1341 | 75 | 1.000 | V_{1} | | |
| cardona-qft-methods_FO1342 | 75 | 1.000 | V_{2} | | |
| cardona-qft-methods_FO1343 | 75 | 1.000 | { }^{\text {b }} | | |
| cardona-qft-methods_FO1344 | 75 | 0.997 | R(G):=\{(V, U) \mid V, U | | |
| cardona-qft-methods_FO1345 | 75 | 0.997 | G\} / \sim | | |
| cardona-qft-methods_FO1346 | 75 | 1.000 | { }^{\mathrm{b}} | | |
| cardona-qft-methods_FO1347 | 76 | 1.000 | \operatorname{Ind}_{G}(A) | | |
| cardona-qft-methods_FO1348 | 76 | 1.000 | V_{0} | | |
| cardona-qft-methods_FO1349 | 76 | 1.000 | m_{V_{0}}^{+}-m_{V_{0}}^{-}>0 | | |
| cardona-qft-methods_FO1350 | 76 | 1.000 | q | | |
| cardona-qft-methods_FO1351 | 76 | 1.000 | q= | | |
| cardona-qft-methods_FO1352 | 76 | 0.582 | l^{2} | | |
| cardona-qft-methods_FO1353 | 76 | 1.000 | V_{0}=\mathbb{C} | | |
| cardona-qft-methods_FO1354 | 76 | 1.000 | V_{1}=\mathbb{C} | | |
| cardona-qft-methods_FO1355 | 76 | 1.000 | q z=-z | | |
| cardona-qft-methods_FO1356 | 76 | 0.977 | \operatorname{Ker}(T)=V_{0} \oplus V_{1} | | |
| cardona-qft-methods_FO1357 | 76 | 1.000 | \operatorname{Ind}_{G}(T) | | |
| cardona-qft-methods_FO1358 | 77 | 1.000 | D_{j} | | |
| cardona-qft-methods_FO1359 | 77 | 1.000 | C^{\infty}\left(\mathbb{R}^{n}\right) \rightarrow C^{\infty}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1360 | 77 | 0.999 | \alpha=\left(\alpha_{1}, \ldots, \alpha_{n}\right) \in | | |
| cardona-qft-methods_FO1361 | 77 | 1.000 | \mathbb{Z}_{\geq 0}^{n} | | |
| cardona-qft-methods_FO1362 | 77 | 1.000 | a_{\alpha}(x) \in C^{\infty}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1363 | 77 | 1.000 | C_{c}^{\infty}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1364 | 77 | 1.000 | \langle\cdot, \cdot\rangle | | |
| cardona-qft-methods_FO1365 | 78 | 1.000 | H^{k}\left(\mathbb{R}^{n}\right) \subset L^{2}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1366 | 78 | 1.000 | H^{k}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1367 | 78 | 1.000 | L^{2}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1368 | 78 | 1.000 | \Omega \subset \mathbb{R}^{n} | | |
| cardona-qft-methods_FO1369 | 78 | 1.000 | H^{k}(\Omega) | | |
| cardona-qft-methods_FO1370 | 78 | 1.000 | K \subset M | | |
| cardona-qft-methods_FO1371 | 78 | 0.997 | m \geq k | | |
| cardona-qft-methods_FO1372 | 78 | 0.997 | \mathcal{D}: C_{c}^{\infty}\left(\mathbb{R}^{n}\right) \rightarrow C_{c}^{\infty}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1373 | 78 | 1.000 | \mathcal{D}: H_{K}^{m}\left(\mathbb{R}^{n}\right) \rightarrow | | |
| cardona-qft-methods_FO1374 | 78 | 1.000 | K \subset \mathbb{R}^{n} | | |
| cardona-qft-methods_FO1375 | 78 | 1.000 | H_{K}^{m}\left(\mathbb{R}^{n}\right) \hookrightarrow H^{k}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1376 | 78 | 1.000 | m>k | | |
| cardona-qft-methods_FO1377 | 78 | 1.000 | k<m | | |
| cardona-qft-methods_FO1378 | 78 | 1.000 | H_{K}^{m}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1379 | 78 | 1.000 | H_{K}^{m}\left(\mathbb{R}^{n}\right) \rightarrow L^{2}\left(\mathbb{R}^{n}\right) | | |
| cardona-qft-methods_FO1380 | 78 | 1.000 | C^{\infty}\left(\mathbb{R}^{n}, \mathbb{R}^{N}\right) | | |
| cardona-qft-methods_FO1381 | 78 | 1.000 | \mathbb{R}^{N} | | |
| cardona-qft-methods_FO1382 | 78 | 1.000 | L^{2}\left(\mathbb{R}^{n}, \mathbb{R}^{N}\right), H^{k}\left(\mathbb{R}^{n}, \mathbb{R}^{N}\right) | | |
| cardona-qft-methods_FO1383 | 78 | 1.000 | H_{K}^{k}\left(\mathbb{R}^{n}, \mathbb{R}^{N}\right) | | |
| cardona-qft-methods_FO1384 | 79 | 0.998 | \mathcal{D}: C^{\infty}\left(\mathbb{R}^{n}, \mathbb{R}^{N_{1}}\right) \rightarrow C^{\infty}\left(\mathbb{R}^{n}, \mathbb{R}^{N_{2}}\right) | | |
| cardona-qft-methods_FO1385 | 79 | 1.000 | \pi: E \rightarrow M | | |
| cardona-qft-methods_FO1386 | 79 | 1.000 | \pi^{-1}(x) | | |
| cardona-qft-methods_FO1387 | 79 | 1.000 | E=M \times \mathcal{C}^{N} | | |
| cardona-qft-methods_FO1388 | 79 | 1.000 | \mathcal{C}^{N} | | |
| cardona-qft-methods_FO1389 | 79 | 1.000 | s: M \rightarrow E | | |
| cardona-qft-methods_FO1390 | 79 | 1.000 | s(x) \in E_{x} | | |
| cardona-qft-methods_FO1391 | 79 | 1.000 | M \rightarrow \mathcal{C}^{N} | | |
| cardona-qft-methods_FO1392 | 79 | 1.000 | C^{\infty}(M, E) | | |
| cardona-qft-methods_FO1393 | 80 | 1.000 | f \in C^{\infty}(M, E) | | |
| cardona-qft-methods_FO1394 | 80 | 1.000 | \operatorname{supp}(\mathcal{D} f) \subset \operatorname{supp}(f) | | |
| cardona-qft-methods_FO1395 | 80 | 1.000 | \left\{U_{i}\right\}_{i=1}^{m} | | |
| cardona-qft-methods_FO1396 | 80 | 1.000 | U_{i} | | |
| cardona-qft-methods_FO1397 | 80 | 0.881 | C^{\infty}(M, E) \rightarrow C^{\infty}(M, F) | | |
| cardona-qft-methods_FO1398 | 80 | 1.000 | i=1, \ldots, m | | |
| cardona-qft-methods_FO1399 | 80 | 1.000 | \mathcal{D}_{i} | | |
| cardona-qft-methods_FO1400 | 80 | 1.000 | H^{k}(M, E) | | |
| cardona-qft-methods_FO1401 | 80 | 1.000 | \langle\cdot, \cdot\rangle_{k} | | |
| cardona-qft-methods_FO1402 | 80 | 1.000 | C_{k}^{\infty}(M, E) | | |
| cardona-qft-methods_FO1403 | 80 | 1.000 | C_{c}^{\infty}(M, E) | | |
| cardona-qft-methods_FO1404 | 80 | 1.000 | M=\mathbb{R}^{n} | | |
| cardona-qft-methods_FO1405 | 80 | 1.000 | \mathcal{D}: C^{\infty}(M, E) \rightarrow C^{\infty}(M, F) | | |
| cardona-qft-methods_FO1406 | 81 | 1.000 | H_{K}^{m}(M, E) \rightarrow L^{2}(M, F) | | |
| cardona-qft-methods_FO1407 | 81 | 1.000 | x_{0} \in M | | |
| cardona-qft-methods_FO1408 | 81 | 1.000 | \xi \in T_{x_{0}}^{*} M | | |
| cardona-qft-methods_FO1409 | 81 | 1.000 | e \in | | |
| cardona-qft-methods_FO1410 | 81 | 1.000 | E_{x_{0}} | | |
| cardona-qft-methods_FO1411 | 81 | 1.000 | d f_{x_{0}}=\xi | | |
| cardona-qft-methods_FO1412 | 81 | 1.000 | s \in C^{\infty}(M, E) | | |
| cardona-qft-methods_FO1413 | 81 | 1.000 | s\left(x_{0}\right)=e | | |
| cardona-qft-methods_FO1414 | 81 | 1.000 | \sigma_{L}(\mathcal{D})\left(x_{0}, \xi\right) e | | |
| cardona-qft-methods_FO1415 | 81 | 1.000 | e | | |
| cardona-qft-methods_FO1416 | 81 | 1.000 | \sigma_{L}(\mathcal{D})\left(x_{0}, \xi\right) | | |
| cardona-qft-methods_FO1417 | 81 | 1.000 | E_{x_{0}} \rightarrow F_{x_{0}} | | |
| cardona-qft-methods_FO1418 | 81 | 1.000 | T_{x_{0}} M | | |
| cardona-qft-methods_FO1419 | 81 | 0.999 | \sigma_{L}(\mathcal{D})\left(x_{0}, \xi\right)\left(x_{0} \in M, \xi \in T_{x_{0}}^{*} M\right) | | |
| cardona-qft-methods_FO1420 | 81 | 1.000 | \operatorname{Hom}\left(E_{x}, F_{x}\right) | | |
| cardona-qft-methods_FO1421 | 82 | 1.000 | \pi: T^{*} M \rightarrow M | | |
| cardona-qft-methods_FO1422 | 82 | 1.000 | \pi^{*} E | | |
| cardona-qft-methods_FO1423 | 82 | 1.000 | (x, \xi) \in T^{*} M | | |
| cardona-qft-methods_FO1424 | 82 | 1.000 | \sigma_{L}(\mathcal{D})(x, \xi) | | |
| cardona-qft-methods_FO1425 | 82 | 1.000 | \sigma_{L}(\mathcal{D}) | | |
| cardona-qft-methods_FO1426 | 82 | 1.000 | \operatorname{Hom}\left(\pi^{*} E, \pi^{*} F\right) | | |
| cardona-qft-methods_FO1427 | 82 | 1.000 | \xi \neq 0 | | |
| cardona-qft-methods_FO1428 | 82 | 0.999 | \sigma_{L}(\Delta) | | |
| cardona-qft-methods_FO1429 | 82 | 0.999 | \xi=\left(\xi_{1}, \ldots, \xi_{n}\right) \neq 0 | | |
| cardona-qft-methods_FO1430 | 82 | 0.999 | \mathcal{D} f=u | | |
| cardona-qft-methods_FO1431 | 82 | 0.999 | u \in C^{\infty}(M, F) | | |
| cardona-qft-methods_FO1432 | 82 | 0.999 | \operatorname{Ind}(\mathcal{D}) | | |
| cardona-qft-methods_FO1433 | 82 | 1.000 | \sigma_{L}\left(\mathcal{D}_{1}\right)=\sigma_{L}\left(\mathcal{D}_{2}\right) | | |
| cardona-qft-methods_FO1434 | 82 | 1.000 | \operatorname{Ind}\left(\mathcal{D}_{1}\right)=\operatorname{Ind}\left(\mathcal{D}_{2}\right) | | |
| cardona-qft-methods_FO1435 | 83 | 1.000 | M=S^{1} | | |
| cardona-qft-methods_FO1436 | 83 | 1.000 | \operatorname{SEll}(E, F) | | |
| cardona-qft-methods_FO1437 | 83 | 1.000 | \sigma(x, \xi) \in \operatorname{Hom}\left(\pi^{*} E, \pi^{*} F\right) | | |
| cardona-qft-methods_FO1438 | 83 | 1.000 | { }^{14,15} | | |
| cardona-qft-methods_FO1439 | 83 | 1.000 | { }^{6,7} | | |
| cardona-qft-methods_FO1440 | 83 | 1.000 | { }^{9,23} | | |
| cardona-qft-methods_FO1441 | 83 | 0.942 | \mathrm{t}-\operatorname{Ind}(\mathcal{D}) | | |
| cardona-qft-methods_FO1442 | 84 | 1.000 | \operatorname{Ind}(\mathcal{D})=\mathrm{t}-\operatorname{Ind}\left(\sigma_{L}(\mathcal{D})\right) | | |
| cardona-qft-methods_FO1443 | 84 | 1.000 | \mathcal{D} f=0 | | |
| cardona-qft-methods_FO1444 | 84 | 1.000 | \mathcal{D}^{*} u=0 | | |
| cardona-qft-methods_FO1445 | 84 | 1.000 | \sigma(x): E_{x} \rightarrow F_{x} | | |
| cardona-qft-methods_FO1446 | 84 | 1.000 | K \subset X | | |
| cardona-qft-methods_FO1447 | 84 | 1.000 | \sigma_{1}: E_{1} \rightarrow F_{1} | | |
| cardona-qft-methods_FO1448 | 84 | 0.999 | \sigma_{2}: E_{2} \rightarrow F_{2} | | |
| cardona-qft-methods_FO1449 | 84 | 0.999 | k_{1}, k_{2} \geq 0 | | |
| cardona-qft-methods_FO1450 | 85 | 1.000 | \sigma_{1} \sim \sigma_{2} | | |
| cardona-qft-methods_FO1451 | 85 | 1.000 | K(X) | | |
| cardona-qft-methods_FO1452 | 85 | 1.000 | \sigma_{1}, \sigma_{2}: E \rightarrow F | | |
| cardona-qft-methods_FO1453 | 85 | 1.000 | (E, F) | | |
| cardona-qft-methods_FO1454 | 85 | 1.000 | E-F | | |
| cardona-qft-methods_FO1455 | 85 | 1.000 | X=\{p t\} | | |
| cardona-qft-methods_FO1456 | 85 | 1.000 | E_{x} \rightarrow F_{x} | | |
| cardona-qft-methods_FO1457 | 85 | 1.000 | \sigma(\mathcal{D}) | | |
| cardona-qft-methods_FO1458 | 86 | 1.000 | X=T^{*} M | | |
| cardona-qft-methods_FO1459 | 86 | 1.000 | K\left(T^{*} M\right) | | |
| cardona-qft-methods_FO1460 | 86 | 1.000 | j: Y \hookrightarrow X | | |
| cardona-qft-methods_FO1461 | 86 | 1.000 | i:\{p t\} \hookrightarrow \mathcal{C}^{N} | | |
| cardona-qft-methods_FO1462 | 86 | 1.000 | M \hookrightarrow \mathbb{R}^{N} | | |
| cardona-qft-methods_FO1463 | 87 | 0.971 | i_{!} | | |
| cardona-qft-methods_FO1464 | 87 | 1.000 | j: M \hookrightarrow \mathbb{R}^{N} | | |
| cardona-qft-methods_FO1465 | 87 | 1.000 | g \in G | | |
| cardona-qft-methods_FO1466 | 87 | 1.000 | \phi(g): M \rightarrow M | | |
| cardona-qft-methods_FO1467 | 87 | 1.000 | \phi\left(g_{1}\right) \circ \phi\left(g_{2}\right)=\phi\left(g_{1} g_{2}\right) | | |
| cardona-qft-methods_FO1468 | 87 | 1.000 | g \cdot x | | |
| cardona-qft-methods_FO1469 | 87 | 1.000 | g \cdot e | | |
| cardona-qft-methods_FO1470 | 87 | 1.000 | \phi(g)(x) | | |
| cardona-qft-methods_FO1471 | 87 | 1.000 | \psi(g)(e) | | |
| cardona-qft-methods_FO1472 | 87 | 1.000 | l_{g}: L^{2}(M, E) \rightarrow L^{2}(M, E) | | |
| cardona-qft-methods_FO1473 | 87 | 1.000 | L^{2}(G) | | |
| cardona-qft-methods_FO1474 | 87 | 1.000 | g \cdot \mathcal{D}=\mathcal{D} \cdot g | | |
| cardona-qft-methods_FO1475 | 88 | 1.000 | K_{G}(X) | | |
| cardona-qft-methods_FO1476 | 88 | 1.000 | M \subset T^{*} M | | |
| cardona-qft-methods_FO1477 | 88 | 1.000 | \sigma_{L} \in | | |
| cardona-qft-methods_FO1478 | 88 | 0.612 | K_{G}\left(T^{*} M\right) | | |
| cardona-qft-methods_FO1479 | 88 | 0.612 | \mathrm{t}-\operatorname{Ind}\left(\sigma_{L}(\mathcal{D})\right) | | |
| cardona-qft-methods_FO1480 | 88 | 1.000 | \operatorname{Ind}_{G}(\mathcal{D})=\mathrm{t}-\operatorname{Ind}_{G}\left(\sigma_{L}(\mathcal{D})\right) | | |
| cardona-qft-methods_FO1481 | 89 | 1.000 | \sigma: \pi^{*} E \rightarrow \pi^{*} F | | |
| cardona-qft-methods_FO1482 | 89 | 0.920 | C^{\infty}(N) \rightarrow C^{\infty}(N) | | |
| cardona-qft-methods_FO1483 | 89 | 1.000 | \left(x_{1}, \ldots, x_{n}\right) | | |
| cardona-qft-methods_FO1484 | 89 | 0.558 | \left(y_{1}, \cdots, y_{r}\right) | | |
| cardona-qft-methods_FO1485 | 89 | 0.558 | \left(x_{1}, \ldots, x_{n}, y_{1}, \ldots, y_{r}\right) | | |
| cardona-qft-methods_FO1486 | 89 | 1.000 | \tilde{\mathcal{D}} | | |
| cardona-qft-methods_FO1487 | 90 | 1.000 | \operatorname{Ker}(\tilde{\mathcal{D}}) | | |
| cardona-qft-methods_FO1488 | 90 | 1.000 | \operatorname{Coker}(\tilde{\mathcal{D}}) | | |
| cardona-qft-methods_FO1489 | 90 | 1.000 | \operatorname{dim} V | | |
| cardona-qft-methods_FO1490 | 90 | 1.000 | \operatorname{Ind}(\tilde{\mathcal{D}}) | | |
| cardona-qft-methods_FO1491 | 90 | 1.000 | \widehat{R}(G) | | |
| cardona-qft-methods_FO1492 | 90 | 1.000 | N=M / G | | |
| cardona-qft-methods_FO1493 | 90 | 1.000 | \xi \in T^{*} M | | |
| cardona-qft-methods_FO1494 | 90 | 0.994 | v \in T \mathcal{O}(x) | | |
| cardona-qft-methods_FO1495 | 90 | 0.994 | \xi(v)=0 | | |
| cardona-qft-methods_FO1496 | 90 | 1.000 | T_{G}^{*} M | | |
| cardona-qft-methods_FO1497 | 90 | 1.000 | T_{G, x}^{*} M:=T_{G}^{*} M \cap T_{x}^{*} M | | |
| cardona-qft-methods_FO1498 | 91 | 1.000 | 0 \neq \xi \in T_{G}^{*} M | | |
| cardona-qft-methods_FO1499 | 91 | 0.999 | \operatorname{Ker}(\mathcal{D}) | | |
| cardona-qft-methods_FO1500 | 91 | 0.999 | \operatorname{Coker}(\mathcal{D}) | | |
| cardona-qft-methods_FO1501 | 91 | 1.000 | m_{V}^{ \pm} \in | | |
| cardona-qft-methods_FO1502 | 91 | 1.000 | \mathbb{Z}_{\geq 0} | | |
| cardona-qft-methods_FO1503 | 91 | 1.000 | m_{V}^{ \pm} \in \mathbb{Z}_{\geq 0} | | |
| cardona-qft-methods_FO1504 | 91 | 1.000 | T_{G, x}^{*} M | | |
| cardona-qft-methods_FO1505 | 92 | 1.000 | K_{G}\left(T_{G}^{*} M\right) | | |
| cardona-qft-methods_FO1506 | 92 | 1.000 | \sigma \in K_{G}\left(T_{G}^{*} M\right) | | |
| cardona-qft-methods_FO1507 | 92 | 1.000 | \sigma_{L}(D)=\sigma | | |
| cardona-qft-methods_FO1508 | 93 | 1.000 | \mathbb{R} | | |
| cardona-qft-methods_FO1509 | 93 | 1.000 | W | | |
| cardona-qft-methods_FO1510 | 93 | 1.000 | v \in V | | |
| cardona-qft-methods_FO1511 | 93 | 0.994 | c: V \rightarrow \operatorname{End}(W) | | |
| cardona-qft-methods_FO1512 | 93 | 1.000 | \mathbb{R}^{3} | | |
| cardona-qft-methods_FO1513 | 93 | 1.000 | \mathcal{C}^{2} | | |
| cardona-qft-methods_FO1514 | 93 | 1.000 | V^{\mathcal{C}}=V \otimes_{\mathbb{R}} \mathcal{C} | | |
| cardona-qft-methods_FO1515 | 93 | 1.000 | V^{\mathcal{C}} | | |
| cardona-qft-methods_FO1516 | 93 | 1.000 | \varepsilon(v): W \rightarrow W | | |
| cardona-qft-methods_FO1517 | 93 | 1.000 | v | | |
| cardona-qft-methods_FO1518 | 93 | 1.000 | V^{*} | | |
| cardona-qft-methods_FO1519 | 93 | 1.000 | \iota_{v}: W \rightarrow W | | |
| cardona-qft-methods_FO1520 | 93 | 1.000 | c: v \mapsto c(v) | | |
| cardona-qft-methods_FO1521 | 94 | 1.000 | E \rightarrow | | |
| cardona-qft-methods_FO1522 | 94 | 0.999 | v \in T^{*} M | | |
| cardona-qft-methods_FO1523 | 94 | 0.999 | c(v)^{2}=-|v|^{2} \mathrm{Id} | | |
| cardona-qft-methods_FO1524 | 94 | 0.999 | M=\mathbb{R}^{3} | | |
| cardona-qft-methods_FO1525 | 94 | 0.999 | E=\mathbb{R}^{3} \times \mathcal{C}^{2} | | |
| cardona-qft-methods_FO1526 | 94 | 1.000 | E=\Lambda^{*}\left(T^{*} M \otimes \mathcal{C}\right) | | |
| cardona-qft-methods_FO1527 | 94 | 1.000 | \Omega^{*}(M) | | |
| cardona-qft-methods_FO1528 | 94 | 1.000 | \omega \in \Omega^{*}(M) | | |
| cardona-qft-methods_FO1529 | 94 | 0.993 | \nabla: C^{\infty}(M, E) \rightarrow \Omega^{1}(M, E) | | |
| cardona-qft-methods_FO1530 | 94 | 1.000 | u \in T M, v \in T^{*} M, s \in C^{\infty}(M, E) | | |
| cardona-qft-methods_FO1531 | 95 | 0.949 | e_{1}, \ldots, e_{n} | | |
| cardona-qft-methods_FO1532 | 95 | 0.949 | T M .^{\mathrm{c}} | | |
| cardona-qft-methods_FO1533 | 95 | 1.000 | d: \Omega^{*}(M, E) \rightarrow | | |
| cardona-qft-methods_FO1534 | 95 | 1.000 | \Omega^{*+1}(M, E) | | |
| cardona-qft-methods_FO1535 | 95 | 0.997 | \Omega^{*}(M, E) | | |
| cardona-qft-methods_FO1536 | 95 | 1.000 | { }^{\mathrm{c}} | | |
| cardona-qft-methods_FO1537 | 97 | 1.000 | C^{\infty}\left(M, E^{+}\right) | | |
| cardona-qft-methods_FO1538 | 97 | 0.950 | \left.C^{\infty}\left(M, E^{-}\right)\right) | | |
| cardona-qft-methods_FO1539 | 97 | 0.950 | \mathcal{D}^{+} | | |
| cardona-qft-methods_FO1540 | 97 | 0.950 | \mathcal{D}^{-} | | |
| cardona-qft-methods_FO1541 | 97 | 1.000 | \mathcal{D}=\mathcal{D}^{+} \oplus \mathcal{D}^{-} | | |
| cardona-qft-methods_FO1542 | 97 | 1.000 | \mathcal{D}^{+}: C^{\infty}\left(M, E^{+}\right) \rightarrow | | |
| cardona-qft-methods_FO1543 | 97 | 0.827 | C^{\infty}\left(M, E^{-}\right) | | |
| cardona-qft-methods_FO1544 | 97 | 1.000 | E=\Lambda^{*}\left(T^{*} M \otimes\right. | | |
| cardona-qft-methods_FO1545 | 97 | 0.997 | \mathcal{C} | | |
| cardona-qft-methods_FO1546 | 97 | 0.998 | \operatorname{Ind}\left(\mathcal{D}^{+}\right) | | |
| cardona-qft-methods_FO1547 | 97 | 1.000 | \operatorname{dim} M=n=2 l | | |
| cardona-qft-methods_FO1548 | 97 | 1.000 | *: E \rightarrow E | | |
| cardona-qft-methods_FO1549 | 97 | 1.000 | \Gamma: E \rightarrow E | | |
| cardona-qft-methods_FO1550 | 97 | 0.998 | \Gamma^{2}=1 | | |
| cardona-qft-methods_FO1551 | 97 | 1.000 | \{1,-1\} | | |
| cardona-qft-methods_FO1552 | 97 | 1.000 | E^{+} | | |
| cardona-qft-methods_FO1553 | 97 | 1.000 | E^{-} | | |
| cardona-qft-methods_FO1554 | 98 | 0.925 | \mathcal{D}^{ \pm} | | |
| cardona-qft-methods_FO1555 | 99 | 0.963 | \mathfrak{g}=\operatorname{Lie} S^{1} | | |
| cardona-qft-methods_FO1556 | 99 | 1.000 | \mathbf{v}: M \rightarrow | | |
| cardona-qft-methods_FO1557 | 99 | 0.998 | \mathbf{v}(x) \equiv 1 | | |
| cardona-qft-methods_FO1558 | 99 | 1.000 | G=S^{1} | | |
| cardona-qft-methods_FO1559 | 99 | 1.000 | M=\mathcal{C} | | |
| cardona-qft-methods_FO1560 | 99 | 1.000 | \left(e^{i t}, z\right) \mapsto e^{i t} z | | |
| cardona-qft-methods_FO1561 | 99 | 1.000 | v(x) | | |
| cardona-qft-methods_FO1562 | 99 | 0.885 | (M, \mathbf{v}) | | |
| cardona-qft-methods_FO1563 | 99 | 0.885 | \mathbf{v} | | |
| cardona-qft-methods_FO1564 | 99 | 1.000 | \pi: T_{G}^{*} M \rightarrow M | | |
| cardona-qft-methods_FO1565 | 99 | 1.000 | \pi^{*} E=\pi^{*} E^{+} \oplus \pi^{*} E^{-} | | |
| cardona-qft-methods_FO1566 | 99 | 1.000 | x \in M, \xi \in T^{*} M | | |
| cardona-qft-methods_FO1567 | 100 | 1.000 | (x, \xi) \in T_{G}^{*} M | | |
| cardona-qft-methods_FO1568 | 100 | 1.000 | c(\xi+v(x)) | | |
| cardona-qft-methods_FO1569 | 100 | 1.000 | (x, \xi) \in | | |
| cardona-qft-methods_FO1570 | 100 | 1.000 | v(x) \neq 0, \xi \neq 0 | | |
| cardona-qft-methods_FO1571 | 100 | 0.572 | (E, \mathbf{v}) | | |
| cardona-qft-methods_FO1572 | 100 | 1.000 | \mathrm{t}-\operatorname{Ind}_{G}(E, \mathbf{v}) | | |
| cardona-qft-methods_FO1573 | 100 | 1.000 | { }^{24,25} | | |
| cardona-qft-methods_FO1574 | 100 | 1.000 | c(\xi) | | |
| cardona-qft-methods_FO1576 | 100 | 1.000 | f(x) v(x) | | |
| cardona-qft-methods_FO1577 | 100 | 1.000 | f: M \rightarrow[0, \infty) | | |
| cardona-qft-methods_FO1578 | 100 | 1.000 | M, E | | |
| cardona-qft-methods_FO1579 | 100 | 1.000 | \nabla | | |
| cardona-qft-methods_FO1580 | 100 | 0.817 | M, E, \nabla, \mathbf{v} | | |
| cardona-qft-methods_FO1581 | 101 | 0.994 | (M, E, \nabla, \mathbf{v}) | | |
| cardona-qft-methods_FO1582 | 101 | 1.000 | \mathcal{D}_{f v}^{+} | | |
| cardona-qft-methods_FO1583 | 101 | 1.000 | \mathcal{D}_{f v} | | |
| cardona-qft-methods_FO1584 | 101 | 1.000 | \operatorname{Ker}\left(\mathcal{D}_{f v}^{+}\right) | | |
| cardona-qft-methods_FO1585 | 101 | 1.000 | \operatorname{Coker}\left(\mathcal{D}_{f v}^{+}\right) | | |
| cardona-qft-methods_FO1586 | 101 | 1.000 | D_{f v}^{+} | | |
| cardona-qft-methods_FO1587 | 101 | 1.000 | m_{V}^{ \pm} | | |
| cardona-qft-methods_FO1588 | 101 | 1.000 | \operatorname{Ker} \mathcal{D}_{f v}^{ \pm} | | |
| cardona-qft-methods_FO1589 | 101 | 1.000 | V \in \operatorname{Irr}(G) | | |
| cardona-qft-methods_FO1590 | 101 | 1.000 | m_{V}^{+}-m_{V}^{-}(V \in \operatorname{Irr}(G)) | | |
| cardona-qft-methods_FO1591 | 101 | 0.611 | (\mathcal{D}, \mathbf{v}) | | |
| cardona-qft-methods_FO1592 | 102 | 0.666 | M, \mathbf{v} | | |
| cardona-qft-methods_FO1593 | 102 | 1.000 | \sigma_{1} | | |
| cardona-qft-methods_FO1594 | 102 | 1.000 | \sigma_{2} | | |
| cardona-qft-methods_FO1595 | 102 | 1.000 | E^{ \pm} | | |
| cardona-qft-methods_FO1596 | 102 | 1.000 | f \equiv 1 | | |
| cardona-qft-methods_FO1597 | 102 | 1.000 | \mathcal{D}_{v} | | |
| cardona-qft-methods_FO1598 | 102 | 1.000 | \mathcal{D}_{v}^{2} | | |
| cardona-qft-methods_FO1599 | 102 | 1.000 | \operatorname{Ind}_{G}(\mathcal{D}, \mathbf{v}) | | |
| cardona-qft-methods_FO1600 | 103 | 0.854 | \Sigma \subset M | | |
| cardona-qft-methods_FO1601 | 103 | 1.000 | M \backslash \Sigma | | |
| cardona-qft-methods_FO1602 | 103 | 1.000 | M_{1} | | |
| cardona-qft-methods_FO1603 | 103 | 1.000 | M_{2} | | |
| cardona-qft-methods_FO1604 | 103 | 1.000 | \Sigma | | |
| cardona-qft-methods_FO1605 | 103 | 1.000 | M_{j}(j=1,2) | | |
| cardona-qft-methods_FO1606 | 103 | 1.000 | \mathbf{v}_{j} | | |
| cardona-qft-methods_FO1607 | 103 | 0.783 | M_{j} | | |
| cardona-qft-methods_FO1608 | 103 | 0.783 | \left(M_{j}, \mathbf{v}_{j}\right)(j=1,2) | | |
| cardona-qft-methods_FO1609 | 103 | 1.000 | E_{j} | | |
| cardona-qft-methods_FO1610 | 103 | 1.000 | \mathcal{D}_{j}(j=1,2) | | |
| cardona-qft-methods_FO1611 | 104 | 0.663 | K K | | |
| cardona-qft-methods_FO1612 | 107 | 0.374 | { }^{\text {AM11a }, \text { AM11b }, \text { AM11c }} | | |
| cardona-qft-methods_FO1613 | 107 | 1.000 | C_{G}(t) | | |
| cardona-qft-methods_FO1614 | 107 | 0.987 | { }^{\text {Mar10 }} | | |
| cardona-qft-methods_FO1615 | 108 | 1.000 | \mathbb{C}\left[x_{1}, \ldots, x_{n}\right] | | |
| cardona-qft-methods_FO1616 | 108 | 1.000 | \mathbb{A}_{\mathbb{C}}^{n}\left(=\mathbb{C}^{n}\right) | | |
| cardona-qft-methods_FO1617 | 108 | 1.000 | \mathbb{C}\left[z_{0}, \ldots, z_{n}\right] | | |
| cardona-qft-methods_FO1618 | 108 | 1.000 | \mathbb{P}^{n}=\mathbb{P}_{\mathbb{C}}^{n} | | |
| cardona-qft-methods_FO1619 | 108 | 1.000 | Y \backslash Z | | |
| cardona-qft-methods_FO1620 | 108 | 1.000 | Z | | |
| cardona-qft-methods_FO1621 | 108 | 0.947 | X \rightarrow Y | | |
| cardona-qft-methods_FO1622 | 108 | 1.000 | Y ; X | | |
| cardona-qft-methods_FO1623 | 108 | 1.000 | \mathbb{A}^{n} | | |
| cardona-qft-methods_FO1624 | 108 | 1.000 | f\left(x_{1}, \ldots, x_{n}\right)=0 | | |
| cardona-qft-methods_FO1625 | 108 | 1.000 | \nabla_{p} f | | |
| cardona-qft-methods_FO1626 | 108 | 1.000 | T X | | |
| cardona-qft-methods_FO1627 | 108 | 1.000 | N_{Z} X | | |
| cardona-qft-methods_FO1628 | 108 | 1.000 | \left.T X\right|_{Z} / T Z | | |
| cardona-qft-methods_FO1629 | 108 | 1.000 | X \backslash Z | | |
| cardona-qft-methods_FO1630 | 109 | 1.000 | { }^{\text {Hir64 }} | | |
| cardona-qft-methods_FO1631 | 109 | 0.988 | \operatorname{sum} \chi(X):=\sum_{i}(-1)^{i} \operatorname{dim} H_{c}^{i}(X, \mathbb{Q}) | | |
| cardona-qft-methods_FO1632 | 109 | 1.000 | H_{c} | | |
| cardona-qft-methods_FO1633 | 109 | 1.000 | { }^{\text {Ful93 }} | | |
| cardona-qft-methods_FO1634 | 109 | 1.000 | { }^{\text {Hir75 }} | | |
| cardona-qft-methods_FO1635 | 109 | 1.000 | s_{i} | | |
| cardona-qft-methods_FO1636 | 109 | 1.000 | X=Y \backslash Z | | |
| cardona-qft-methods_FO1637 | 109 | 0.999 | \chi(X)=\chi(Y)-\chi(Z) | | |
| cardona-qft-methods_FO1638 | 109 | 0.999 | X^{\prime} | | |
| cardona-qft-methods_FO1639 | 109 | 0.999 | \chi(X)=\chi\left(X^{\prime}\right) | | |
| cardona-qft-methods_FO1640 | 109 | 1.000 | Z \subseteq X | | |
| cardona-qft-methods_FO1641 | 109 | 1.000 | \chi(X)=\chi(Z)+\chi(X \backslash Z) | | |
| cardona-qft-methods_FO1642 | 109 | 1.000 | \chi(X \times Y)=\chi(X) \cdot \chi(Y) | | |
| cardona-qft-methods_FO1643 | 109 | 1.000 | \chi(X)=\chi(Y) \cdot \chi(F) | | |
| cardona-qft-methods_FO1645 | 110 | 1.000 | \mathbb{Q}, \mathbb{F}_{q} | | |
| cardona-qft-methods_FO1646 | 110 | 0.792 | K_{0}( | | |
| cardona-qft-methods_FO1647 | 110 | 0.792 | ) | | |
| cardona-qft-methods_FO1648 | 110 | 1.000 | [M]=\left[M^{\prime}\right]+\left[M^{\prime \prime}\right] | | |
| cardona-qft-methods_FO1649 | 110 | 1.000 | 0 \rightarrow M^{\prime} \rightarrow M \rightarrow M^{\prime \prime} \rightarrow 0 | | |
| cardona-qft-methods_FO1650 | 110 | 1.000 | { }^{\text {Lev08 }} | | |
| cardona-qft-methods_FO1651 | 110 | 0.590 | 2 \mathrm{in}^{\text {Mar10 }} | | |
| cardona-qft-methods_FO1652 | 110 | 1.000 | Z, X | | |
| cardona-qft-methods_FO1653 | 110 | 1.000 | K_{0}\left(\operatorname{Var}_{k}\right):=\frac{\text { Free abelian group on isom. classes of quasi-proj. } k \text {-varieties }}{\langle[X]=[Z]+[X \backslash Z] \text { for every closed embedding } Z \subseteq X\rangle} | | |
| cardona-qft-methods_FO1654 | 110 | 1.000 | [X] \cdot[Y]=\left[X \times_{k} Y\right] | | |
| cardona-qft-methods_FO1655 | 110 | 0.995 | K_{0}\left(\operatorname{Var}_{k}\right) | | |
| cardona-qft-methods_FO1656 | 110 | 1.000 | k=\mathbb{C} | | |
| cardona-qft-methods_FO1657 | 111 | 1.000 | [X] | | |
| cardona-qft-methods_FO1658 | 111 | 0.916 | K_{0}(\operatorname{Var})\left({ }^{\text {Bit04 }}\right) | | |
| cardona-qft-methods_FO1659 | 111 | 1.000 | e(p)=1 | | |
| cardona-qft-methods_FO1660 | 111 | 1.000 | e(X)=e\left(X^{\prime}\right) | | |
| cardona-qft-methods_FO1661 | 111 | 1.000 | e(X)=e(Z)+e(X \backslash Z) | | |
| cardona-qft-methods_FO1662 | 111 | 1.000 | e(X \times Y)=e(X) e(Y) | | |
| cardona-qft-methods_FO1663 | 111 | 0.968 | K_{0}(\operatorname{Var}) \rightarrow R | | |
| cardona-qft-methods_FO1664 | 111 | 0.970 | ) \rightarrow \mathbb{Z} | | |
| cardona-qft-methods_FO1665 | 111 | 0.621 | [X] \in K_{0}(\operatorname{Var}) | | |
| cardona-qft-methods_FO1666 | 111 | 0.623 | K_{0}(\mathrm{Var}) | | |
| cardona-qft-methods_FO1667 | 111 | 1.000 | \mathbb{Z}[u, v] | | |
| cardona-qft-methods_FO1668 | 111 | 1.000 | K\left(\operatorname{Var}_{\mathbb{Z}}\right) \rightarrow \mathbb{Z} | | |
| cardona-qft-methods_FO1669 | 111 | 1.000 | \mathbb{F}_{q} | | |
| cardona-qft-methods_FO1670 | 112 | 1.000 | { }^{\text {Bit04 }} | | |
| cardona-qft-methods_FO1671 | 112 | 1.000 | Z \subset X | | |
| cardona-qft-methods_FO1672 | 112 | 1.000 | \widetilde{X} \rightarrow X | | |
| cardona-qft-methods_FO1673 | 112 | 1.000 | [X]=[Z]+[X \backslash Z] | | |
| cardona-qft-methods_FO1674 | 112 | 1.000 | \mathbb{L}:= | | |
| cardona-qft-methods_FO1675 | 112 | 0.994 | \left[\mathbb{A}^{1}\right] | | |
| cardona-qft-methods_FO1676 | 112 | 0.994 | \mathbb{Z}[\mathbb{L}] \subseteq K_{0}( | | |
| cardona-qft-methods_FO1677 | 112 | 1.000 | \mathbb{Z}[\mathbb{L}] | | |
| cardona-qft-methods_FO1678 | 112 | 1.000 | \widetilde{X} | | |
| cardona-qft-methods_FO1679 | 112 | 1.000 | [\widetilde{X}] | | |
| cardona-qft-methods_FO1680 | 112 | 1.000 | [Z] | | |
| cardona-qft-methods_FO1681 | 113 | 1.000 | [X] \in \mathbb{Z}[\mathbb{L}] \subseteq K_{0}\left(\operatorname{Var}_{\mathbb{Z}}\right) | | |
| cardona-qft-methods_FO1682 | 113 | 0.644 | \chi(X)=\sum_{i} a_{i} | | |
| cardona-qft-methods_FO1683 | 113 | 0.984 | \mathbb{F}_{1} | | |
| cardona-qft-methods_FO1685 | 113 | 1.000 | c_{\mathrm{SM}}(X) | | |
| cardona-qft-methods_FO1686 | 113 | 1.000 | A_{*} X | | |
| cardona-qft-methods_FO1687 | 113 | 1.000 | { }^{\text {Ful84b }} | | |
| cardona-qft-methods_FO1688 | 113 | 1.000 | A_{*} \mathbb{P}^{n} | | |
| cardona-qft-methods_FO1689 | 113 | 1.000 | \left[\mathbb{P}^{0}\right], \ldots,\left[\mathbb{P}^{n}\right] | | |
| cardona-qft-methods_FO1690 | 113 | 0.950 | r=\operatorname{dim} X | | |
| cardona-qft-methods_FO1691 | 114 | 1.000 | c_{i}(E) \cap[X] | | |
| cardona-qft-methods_FO1692 | 114 | 0.994 | \operatorname{rk} E-i+1 | | |
| cardona-qft-methods_FO1693 | 114 | 1.000 | { }^{\text {Ful84a }} | | |
| cardona-qft-methods_FO1694 | 114 | 0.988 | c_{\operatorname{dim} X}(T X) \cap[X] | | |
| cardona-qft-methods_FO1695 | 114 | 0.981 | \operatorname{dim} X | | |
| cardona-qft-methods_FO1696 | 114 | 1.000 | \int | | |
| cardona-qft-methods_FO1697 | 114 | 1.000 | \chi(X)<0 | | |
| cardona-qft-methods_FO1698 | 114 | 0.885 | { }^{\text {Mac74 }} | | |
| cardona-qft-methods_FO1699 | 115 | 0.594 | \left(,^{\mathrm{BS} 81 \mathrm{AB} 08}\right) | | |
| cardona-qft-methods_FO1700 | 115 | 0.987 | c_{\mathrm{SM}} | | |
| cardona-qft-methods_FO1701 | 115 | 0.987 | c_{\mathrm{SM}}(\varphi) | | |
| cardona-qft-methods_FO1702 | 115 | 1.000 | \varphi=\sum m_{i} \mathbb{1}_{Z_{i}} | | |
| cardona-qft-methods_FO1703 | 115 | 1.000 | C(X) | | |
| cardona-qft-methods_FO1704 | 115 | 1.000 | C | | |
| cardona-qft-methods_FO1705 | 115 | 1.000 | f: X \rightarrow Y | | |
| cardona-qft-methods_FO1706 | 115 | 1.000 | C(X) \rightarrow C(Y) | | |
| cardona-qft-methods_FO1707 | 115 | 1.000 | p \in Y | | |
| cardona-qft-methods_FO1708 | 115 | 1.000 | X, c_{\mathrm{SM}}: C(X) \rightarrow A_{*} X | | |
| cardona-qft-methods_FO1709 | 115 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{1}_{X}\right)=c(T X) \cap[X] | | |
| cardona-qft-methods_FO1710 | 115 | 1.000 | \varphi \in C(X) | | |
| cardona-qft-methods_FO1711 | 115 | 1.000 | c_{\mathrm{SM}}\left(f_{*} \varphi\right)=f_{*} c_{\mathrm{SM}}(\varphi) | | |
| cardona-qft-methods_FO1712 | 115 | 0.549 | { }^{\text {Ken90Alu06 }} | | |
| cardona-qft-methods_FO1713 | 115 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{1}_{X}\right) | | |
| cardona-qft-methods_FO1714 | 115 | 1.000 | c_{\mathrm{SM}}(Y) | | |
| cardona-qft-methods_FO1715 | 115 | 0.998 | c_{\mathrm{SM}}\left(\mathbb{1}_{Y}\right) | | |
| cardona-qft-methods_FO1716 | 115 | 0.821 | \kappa: X \rightarrow\{\mathrm{pt}\} | | |
| cardona-qft-methods_FO1717 | 116 | 0.736 | { }^{\text {Kwi92 }} | | |
| cardona-qft-methods_FO1718 | 116 | 0.736 | { }^{\text {Alu06 }} | | |
| cardona-qft-methods_FO1719 | 116 | 1.000 | c_{\mathrm{SM}}\left(X^{\prime}\right) | | |
| cardona-qft-methods_FO1720 | 116 | 1.000 | A_{*} X \cong A_{*} X^{\prime} | | |
| cardona-qft-methods_FO1721 | 116 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{1}_{X^{\prime}}\right) | | |
| cardona-qft-methods_FO1722 | 116 | 0.999 | \mathbb{P}^{1} | | |
| cardona-qft-methods_FO1723 | 116 | 0.999 | c_{\mathrm{SM}}\left(\mathbb{P}^{1}\right)=\left[\mathbb{P}^{1}\right]+ | | |
| cardona-qft-methods_FO1724 | 116 | 1.000 | 2\left[\mathbb{P}^{0}\right] | | |
| cardona-qft-methods_FO1725 | 116 | 0.974 | T \mathbb{P}^{n} | | |
| cardona-qft-methods_FO1726 | 116 | 1.000 | \int c_{\mathrm{SM}}\left(\mathbb{P}^{n}\right)=\binom{n+1}{n}=n+1=\chi\left(\mathbb{P}^{n}\right) | | |
| cardona-qft-methods_FO1727 | 116 | 1.000 | H | | |
| cardona-qft-methods_FO1728 | 116 | 1.000 | H^{i} | | |
| cardona-qft-methods_FO1729 | 116 | 1.000 | \left[\mathbb{P}^{n-i}\right] | | |
| cardona-qft-methods_FO1730 | 116 | 1.000 | H^{n+1}=0 | | |
| cardona-qft-methods_FO1731 | 117 | 1.000 | \mathbb{P}^{2} | | |
| cardona-qft-methods_FO1732 | 117 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{P}^{1}\right) | | |
| cardona-qft-methods_FO1733 | 117 | 0.999 | L_{1}, L_{2} | | |
| cardona-qft-methods_FO1734 | 117 | 1.000 | c_{\mathrm{SM}}(X)=c_{\mathrm{SM}}\left(L_{1} \cup L_{2}\right) | | |
| cardona-qft-methods_FO1735 | 117 | 0.988 | c_{\text {SM }} | | |
| cardona-qft-methods_FO1736 | 117 | 1.000 | { }^{\text {PP01 }} | | |
| cardona-qft-methods_FO1737 | 117 | 1.000 | { }^{\text {AM09 }} | | |
| cardona-qft-methods_FO1738 | 117 | 0.693 | { }^{\text {Alu12 }} | | |
| cardona-qft-methods_FO1739 | 117 | 0.998 | X \subseteq \mathbb{P}^{n} | | |
| cardona-qft-methods_FO1740 | 117 | 0.996 | { }^{\text {Alub }} | | |
| cardona-qft-methods_FO1741 | 117 | 0.980 | \left({ }^{\text {BSY10 }}\right) | | |
| cardona-qft-methods_FO1742 | 117 | 1.000 | \mathbb{P}^{\infty} | | |
| cardona-qft-methods_FO1743 | 117 | 1.000 | \mathbb{Z}[T] | | |
| cardona-qft-methods_FO1744 | 117 | 0.753 | \left({ }^{\text {Alub }}\right) | | |
| cardona-qft-methods_FO1745 | 118 | 1.000 | L(\phi) | | |
| cardona-qft-methods_FO1746 | 118 | 1.000 | \langle G\rangle | | |
| cardona-qft-methods_FO1747 | 118 | 1.000 | \frac{G(\phi)}{\# \operatorname{Aut}(G)} | | |
| cardona-qft-methods_FO1748 | 118 | 1.000 | G(\phi) | | |
| cardona-qft-methods_FO1749 | 118 | 0.970 | { }^{\mathrm{Zee} 10} | | |
| cardona-qft-methods_FO1750 | 118 | 1.000 | p_{i} | | |
| cardona-qft-methods_FO1751 | 118 | 1.000 | \sum_{i} p_{i}=0 | | |
| cardona-qft-methods_FO1752 | 118 | 1.000 | \hat{\phi} | | |
| cardona-qft-methods_FO1753 | 118 | 0.874 | { }^{\text {CM }} | | |
| cardona-qft-methods_FO1754 | 119 | 1.000 | I_{G} | | |
| cardona-qft-methods_FO1755 | 119 | 1.000 | U(G) | | |
| cardona-qft-methods_FO1756 | 119 | 1.000 | \sigma_{n}=\left\{\sum_{i} t_{i}=1\right\} ; \omega_{n} | | |
| cardona-qft-methods_FO1757 | 119 | 1.000 | P_{G}, \Psi_{G} | | |
| cardona-qft-methods_FO1758 | 119 | 1.000 | \Psi_{G} | | |
| cardona-qft-methods_FO1759 | 119 | 0.957 | P_{G}(\underline{t}, p) | | |
| cardona-qft-methods_FO1760 | 119 | 1.000 | s_{C} | | |
| cardona-qft-methods_FO1761 | 119 | 1.000 | D \ell / 2-n \geq 0 | | |
| cardona-qft-methods_FO1762 | 119 | 1.000 | P_{G} | | |
| cardona-qft-methods_FO1763 | 120 | 1.000 | \Gamma(n-D \ell / 2) | | |
| cardona-qft-methods_FO1764 | 120 | 1.000 | M \geq 0 | | |
| cardona-qft-methods_FO1765 | 120 | 1.000 | \hat{X}_{G} | | |
| cardona-qft-methods_FO1766 | 120 | 1.000 | \Psi_{G}=0 | | |
| cardona-qft-methods_FO1767 | 120 | 1.000 | \overline{\mathbb{Q}} | | |
| cardona-qft-methods_FO1768 | 120 | 1.000 | { }^{\text {KZ01 }} | | |
| cardona-qft-methods_FO1769 | 120 | 1.000 | \frac{1}{2 \pi i} | | |
| cardona-qft-methods_FO1770 | 120 | 1.000 | { }^{\text {Bro12 }} | | |
| cardona-qft-methods_FO1771 | 120 | 1.000 | n_{i} \geq 1, n_{r} \geq 2 | | |
| cardona-qft-methods_FO1772 | 120 | 1.000 | \mathbb{Q}\left[\frac{1}{2 \pi i}\right] | | |
| cardona-qft-methods_FO1773 | 120 | 1.000 | \hat{Y}_{G} | | |
| cardona-qft-methods_FO1774 | 120 | 1.000 | \hat{X}_{G} \subseteq \mathbb{A}^{n} | | |
| cardona-qft-methods_FO1775 | 120 | 1.000 | \Psi_{G}(\underline{t})=0 | | |
| cardona-qft-methods_FO1776 | 121 | 1.000 | { }^{\text {BK97 }} | | |
| cardona-qft-methods_FO1777 | 121 | 1.000 | t_{e} | | |
| cardona-qft-methods_FO1778 | 122 | 1.000 | n>0 | | |
| cardona-qft-methods_FO1779 | 123 | 1.000 | \Psi_{G}(\underline{t}) | | |
| cardona-qft-methods_FO1780 | 123 | 0.943 | X_{G} | | |
| cardona-qft-methods_FO1781 | 123 | 0.943 | \mathbb{P}^{n-1} | | |
| cardona-qft-methods_FO1782 | 123 | 0.943 | n= | | |
| cardona-qft-methods_FO1783 | 123 | 1.000 | Y_{G} | | |
| cardona-qft-methods_FO1784 | 123 | 1.000 | b_{1}(G) | | |
| cardona-qft-methods_FO1785 | 123 | 1.000 | G \backslash e | | |
| cardona-qft-methods_FO1786 | 123 | 0.980 | { }^{\text {Pat10 }} | | |
| cardona-qft-methods_FO1787 | 123 | 0.974 | { }^{\text {SMJO } 77} | | |
| cardona-qft-methods_FO1788 | 123 | 0.998 | { }^{\text {MA }} | | |
| cardona-qft-methods_FO1789 | 123 | 1.000 | \left[\hat{Y}_{G}\right] | | |
| cardona-qft-methods_FO1790 | 123 | 1.000 | K_{0}\left(\operatorname{Var}_{\mathbb{Z}}\right) | | |
| cardona-qft-methods_FO1791 | 123 | 1.000 | \mathbb{F}_{q}\left[t_{1}, \ldots, t_{n}\right] | | |
| cardona-qft-methods_FO1792 | 123 | 1.000 | N_{q}(G) | | |
| cardona-qft-methods_FO1793 | 123 | 1.000 | \left(t_{1}, \ldots, t_{n}\right) | | |
| cardona-qft-methods_FO1794 | 123 | 1.000 | \mathbb{F}_{q}^{n} | | |
| cardona-qft-methods_FO1795 | 123 | 1.000 | \Psi_{G}(\bar{t}) \neq 0 | | |
| cardona-qft-methods_FO1796 | 124 | 0.977 | { }^{\text {Sta98 }} | | |
| cardona-qft-methods_FO1797 | 124 | 0.977 | { }^{\text {Ste98 }} | | |
| cardona-qft-methods_FO1798 | 124 | 0.997 | { }^{\text {BB03 }} | | |
| cardona-qft-methods_FO1799 | 124 | 0.999 | { }^{\text {Dor11Sch11 }} | | |
| cardona-qft-methods_FO1800 | 124 | 1.000 | \mathbb{P}^{3} | | |
| cardona-qft-methods_FO1801 | 124 | 1.000 | { }^{\text {BS12 }} | | |
| cardona-qft-methods_FO1802 | 124 | 1.000 | H^{1}(G) | | |
| cardona-qft-methods_FO1803 | 124 | 1.000 | { }^{\text {AM10 }} | | |
| cardona-qft-methods_FO1804 | 124 | 1.000 | { }^{\text {Vak06 }} | | |
| cardona-qft-methods_FO1805 | 124 | 0.948 | K_{0}(\operatorname{Var}) | | |
| cardona-qft-methods_FO1806 | 125 | 0.990 | c_{\mathrm{SM}}\left(X_{G}\right) | | |
| cardona-qft-methods_FO1807 | 125 | 0.749 | \sum_{\text {graphs }{ }_{G}}\langle G\rangle | | |
| cardona-qft-methods_FO1808 | 125 | 0.999 | G_{i} | | |
| cardona-qft-methods_FO1809 | 125 | 1.000 | G_{1} | | |
| cardona-qft-methods_FO1810 | 125 | 1.000 | G_{2} | | |
| cardona-qft-methods_FO1811 | 126 | 1.000 | { }^{\text {AM11a }} | | |
| cardona-qft-methods_FO1812 | 126 | 1.000 | G_{1}, G_{2} | | |
| cardona-qft-methods_FO1813 | 126 | 1.000 | \Psi_{G}=\left(\Psi_{G_{1}}\right)\left(\Psi_{G_{2}}\right) | | |
| cardona-qft-methods_FO1814 | 127 | 1.000 | t_{4} | | |
| cardona-qft-methods_FO1815 | 127 | 0.988 | \left(t_{1}+t_{2}+t_{3}\right)\left(t_{5}+t_{6}+t_{7}\right) | | |
| cardona-qft-methods_FO1816 | 127 | 1.000 | \Psi_{G}\left(t_{1}, \ldots, t_{n}\right)=0 | | |
| cardona-qft-methods_FO1817 | 127 | 1.000 | \mathbb{A}^{n} \backslash \hat{X}_{G} | | |
| cardona-qft-methods_FO1818 | 127 | 1.000 | G=G_{1} \amalg G_{2} | | |
| cardona-qft-methods_FO1819 | 127 | 1.000 | \hat{Y}_{G} \cong \hat{Y}_{G_{1}} \times \hat{Y}_{G_{2}} | | |
| cardona-qft-methods_FO1820 | 127 | 1.000 | \hat{Y}_{G} \cong | | |
| cardona-qft-methods_FO1821 | 127 | 1.000 | \hat{Y}_{G_{1}} \times \hat{Y}_{G_{2}} \times \mathbb{A}^{1} | | |
| cardona-qft-methods_FO1822 | 127 | 1.000 | t_{1}, \ldots, t_{n_{1}} | | |
| cardona-qft-methods_FO1823 | 127 | 1.000 | u_{1}, \ldots, u_{n_{2}} | | |
| cardona-qft-methods_FO1824 | 127 | 1.000 | \Psi_{G}=\Psi_{G_{1}} \Psi_{G_{2}} | | |
| cardona-qft-methods_FO1825 | 127 | 1.000 | \left(t_{1}, \ldots, t_{n_{1}}, u_{1}, \ldots, u_{n_{2}}\right) | | |
| cardona-qft-methods_FO1826 | 127 | 1.000 | \mathbb{A}^{n_{1}+n_{2}} | | |
| cardona-qft-methods_FO1827 | 127 | 1.000 | \left(t_{1}, \ldots, t_{n_{1}}\right) \in \hat{Y}_{G_{1}} | | |
| cardona-qft-methods_FO1828 | 127 | 1.000 | \left(u_{1} \ldots, u_{n_{2}}\right) \in \hat{Y}_{2} | | |
| cardona-qft-methods_FO1829 | 128 | 1.000 | \mathbb{A}^{1} | | |
| cardona-qft-methods_FO1830 | 128 | 1.000 | G \mapsto U(G) | | |
| cardona-qft-methods_FO1831 | 128 | 1.000 | U(G)=U\left(G_{1}\right) U\left(G_{2}\right) | | |
| cardona-qft-methods_FO1832 | 128 | 1.000 | U(G)=U\left(G_{1}\right) U\left(G_{2}\right) U(e) | | |
| cardona-qft-methods_FO1833 | 128 | 1.000 | U(e) | | |
| cardona-qft-methods_FO1834 | 128 | 1.000 | \mathcal{S B}(G) \in \mathbb{Z} | | |
| cardona-qft-methods_FO1835 | 128 | 1.000 | (-1)^{n} | | |
| cardona-qft-methods_FO1836 | 128 | 1.000 | F \rightarrow R | | |
| cardona-qft-methods_FO1837 | 129 | 1.000 | \mathcal{S B}(G) | | |
| cardona-qft-methods_FO1838 | 129 | 1.000 | \chi\left(Y_{G}\right) | | |
| cardona-qft-methods_FO1839 | 129 | 0.960 | \left[Y_{G}\right] | | |
| cardona-qft-methods_FO1840 | 129 | 0.960 | (\mathbb{L}-1) | | |
| cardona-qft-methods_FO1841 | 129 | 1.000 | \chi\left(Y_{G}\right)=0 | | |
| cardona-qft-methods_FO1842 | 129 | 1.000 | \chi\left(Y_{G_{1}}\right) | | |
| cardona-qft-methods_FO1843 | 129 | 1.000 | \chi\left(Y_{G_{2}}\right) | | |
| cardona-qft-methods_FO1844 | 129 | 1.000 | \mathbb{U}(G):=\left[\hat{Y}_{G}\right] | | |
| cardona-qft-methods_FO1845 | 129 | 0.999 | \mathbb{L}=(\mathbb{T}+1) | | |
| cardona-qft-methods_FO1846 | 129 | 1.000 | \mathbb{U}(G) | | |
| cardona-qft-methods_FO1847 | 129 | 0.516 | (\mathbb{T}+1) | | |
| cardona-qft-methods_FO1848 | 129 | 1.000 | \mathbb{T} | | |
| cardona-qft-methods_FO1849 | 129 | 1.000 | \left[\hat{X}_{G}\right],\left[X_{G}\right] | | |
| cardona-qft-methods_FO1850 | 129 | 1.000 | \hat{X} | | |
| cardona-qft-methods_FO1851 | 129 | 0.996 | \mathbb{P}^{n} | | |
| cardona-qft-methods_FO1852 | 129 | 1.000 | F_{\hat{X}}(T):=a_{0}+a_{1} T+\cdots+a_{n} T^{n} | | |
| cardona-qft-methods_FO1853 | 129 | 1.000 | F_{\mathbb{A}^{n}}(T) | | |
| cardona-qft-methods_FO1854 | 130 | 1.000 | F_{\mathbb{A}^{n}}(T)=(1+T)^{n} | | |
| cardona-qft-methods_FO1855 | 130 | 1.000 | F \rightarrow \mathbb{Z}[T] | | |
| cardona-qft-methods_FO1856 | 130 | 1.000 | F \rightarrow | | |
| cardona-qft-methods_FO1857 | 130 | 1.000 | \left[\mathbb{P}^{i}\right] | | |
| cardona-qft-methods_FO1858 | 130 | 1.000 | \left[\mathbb{P}^{j}\right] | | |
| cardona-qft-methods_FO1859 | 130 | 1.000 | \left[\mathbb{P}^{i+j}\right] | | |
| cardona-qft-methods_FO1860 | 130 | 1.000 | i+j | | |
| cardona-qft-methods_FO1861 | 130 | 1.000 | C_{G}(T):= | | |
| cardona-qft-methods_FO1862 | 130 | 0.997 | F_{\hat{Y}_{G}}(T) \in \mathbb{Z}[T] | | |
| cardona-qft-methods_FO1863 | 130 | 0.997 | C_{\mathbb{A}^{1}}(T)=1+T | | |
| cardona-qft-methods_FO1864 | 130 | 1.000 | C_{G}(T)=T(1+T)^{n-1} | | |
| cardona-qft-methods_FO1865 | 130 | 1.000 | t_{1}+\cdots+t_{n} | | |
| cardona-qft-methods_FO1866 | 130 | 1.000 | \mathbb{A}^{n-1} | | |
| cardona-qft-methods_FO1867 | 130 | 1.000 | F_{\mathbb{A}^{r}}(T)=(1+T)^{r} | | |
| cardona-qft-methods_FO1868 | 131 | 1.000 | C_{G}(T) | | |
| cardona-qft-methods_FO1869 | 131 | 1.000 | T^{n-1} | | |
| cardona-qft-methods_FO1870 | 131 | 1.000 | n-b_{1}(G) | | |
| cardona-qft-methods_FO1871 | 131 | 0.975 | C_{G}(T)=(1+T)^{n} | | |
| cardona-qft-methods_FO1872 | 131 | 1.000 | C_{G}(0)=0 | | |
| cardona-qft-methods_FO1873 | 131 | 1.000 | C_{G}^{\prime}(0) | | |
| cardona-qft-methods_FO1874 | 131 | 1.000 | Y_{G}=\mathbb{P}^{n-1} \backslash X_{G} | | |
| cardona-qft-methods_FO1875 | 131 | 1.000 | G^{\prime} | | |
| cardona-qft-methods_FO1876 | 131 | 0.829 | C_{G^{\prime}}(T)=(1+T) C_{G}(T) | | |
| cardona-qft-methods_FO1877 | 131 | 1.000 | C_{G^{\prime}}(T)= | | |
| cardona-qft-methods_FO1878 | 131 | 1.000 | T C_{G}(T) | | |
| cardona-qft-methods_FO1879 | 131 | 0.999 | C_{G}(-1)=0 | | |
| cardona-qft-methods_FO1880 | 131 | 1.000 | n-1 | | |
| cardona-qft-methods_FO1881 | 131 | 1.000 | T(1+T)^{n-1} | | |
| cardona-qft-methods_FO1882 | 131 | 1.000 | C_{G_{1}}(T)=\chi\left(Y_{G_{1}}\right) T+ | | |
| cardona-qft-methods_FO1883 | 131 | 1.000 | C_{G_{2}}(T)=\chi\left(Y_{G_{2}}\right) T+ | | |
| cardona-qft-methods_FO1884 | 131 | 1.000 | \chi\left(Y_{G_{1} \amalg G_{2}}\right)=0 | | |
| cardona-qft-methods_FO1885 | 131 | 1.000 | \chi\left(Y_{G_{1}}\right) \chi\left(Y_{G_{2}}\right) | | |
| cardona-qft-methods_FO1886 | 131 | 1.000 | T^{2} | | |
| cardona-qft-methods_FO1887 | 131 | 0.803 | \pm 1 | | |
| cardona-qft-methods_FO1888 | 131 | 1.000 | { }^{\text {Str11 }} | | |
| cardona-qft-methods_FO1889 | 131 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{1}_{\mathbb{P}^{n-1} \backslash X_{G}}\right) | | |
| cardona-qft-methods_FO1890 | 131 | 1.000 | \left[\mathbb{P}^{k}\right] | | |
| cardona-qft-methods_FO1891 | 131 | 1.000 | T^{k+1} | | |
| cardona-qft-methods_FO1892 | 131 | 0.997 | c_{\mathrm{SM}}\left(\mathbb{1}_{X_{G}}\right) | | |
| cardona-qft-methods_FO1893 | 132 | 1.000 | t_{1} t_{2}+t_{1} t_{3}+t_{2} t_{3} | | |
| cardona-qft-methods_FO1894 | 132 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{1}_{X_{G}}\right)= | | |
| cardona-qft-methods_FO1895 | 132 | 1.000 | 2\left[\mathbb{P}^{0}\right]+2\left[\mathbb{P}^{1}\right] | | |
| cardona-qft-methods_FO1896 | 132 | 1.000 | c_{\mathrm{SM}}\left(\mathbb{1}_{\mathbb{P}^{2} \backslash X_{G}}\right)=\left[\mathbb{P}^{0}\right]+\left[\mathbb{P}^{1}\right]+\left[\mathbb{P}^{2}\right] | | |
| cardona-qft-methods_FO1897 | 132 | 0.651 | C_{G}(T)=T\left(1+T+T^{2}\right) | | |
| cardona-qft-methods_FO1898 | 132 | 1.000 | { }^{\text {Web12 }} | | |
| cardona-qft-methods_FO1899 | 132 | 1.000 | { }^{\text {Bol98 }} | | |
| cardona-qft-methods_FO1900 | 132 | 1.000 | T_{G}(x, y)=x^{i} y^{j} | | |
| cardona-qft-methods_FO1901 | 132 | 0.999 | G / e, G \backslash e | | |
| cardona-qft-methods_FO1902 | 132 | 1.000 | R[\alpha, \beta, \gamma, x, y] | | |
| cardona-qft-methods_FO1903 | 132 | 1.000 | \tau(G)=\gamma^{\# \text { vertices }} | | |
| cardona-qft-methods_FO1904 | 132 | 1.000 | \tau(G)=x \tau(G \backslash e) | | |
| cardona-qft-methods_FO1905 | 132 | 1.000 | \tau(G)=y \tau(G / e) | | |
| cardona-qft-methods_FO1906 | 132 | 0.999 | \tau(G)=\alpha \tau(G / e)+\beta \tau(G \backslash e) | | |
| cardona-qft-methods_FO1907 | 133 | 1.000 | \alpha=\beta=\gamma=1 | | |
| cardona-qft-methods_FO1908 | 133 | 1.000 | b_{0}(G) | | |
| cardona-qft-methods_FO1909 | 134 | 1.000 | x=1-\lambda, y=0 | | |
| cardona-qft-methods_FO1910 | 134 | 1.000 | (1-\lambda)^{2}+(1-\lambda)=(1-\lambda)(2-\lambda) | | |
| cardona-qft-methods_FO1911 | 134 | 1.000 | T_{G}(x, y) | | |
| cardona-qft-methods_FO1912 | 134 | 1.000 | G_{2 e} | | |
| cardona-qft-methods_FO1913 | 134 | 0.998 | x^{2}+x+y | | |
| cardona-qft-methods_FO1914 | 134 | 0.998 | x+y | | |
| cardona-qft-methods_FO1915 | 135 | 0.997 | { }^{\text {AM11b }} | | |
| cardona-qft-methods_FO1916 | 135 | 0.997 | { }^{\text {Alua }} | | |
| cardona-qft-methods_FO1917 | 135 | 0.453 | \mathbb{U}(G)=\mathbb{L} \cdot\left[\hat{Y}_{G \backslash e} \cup \hat{Y}_{G / e}\right]-\mathbb{U}(G \backslash e) | | |
| cardona-qft-methods_FO1918 | 135 | 1.000 | \mathbb{U}\left(G_{2 e}\right)=(\mathbb{T}-1) \cdot \mathbb{U}(G)+\mathbb{T} \cdot \mathbb{U}(G \backslash e)+(\mathbb{T}+1) \cdot \mathbb{U}(G / e) | | |
| cardona-qft-methods_FO1919 | 135 | 1.000 | \hat{Y}_{G \backslash e} \cup \hat{Y}_{G / e} | | |
| cardona-qft-methods_FO1920 | 135 | 1.000 | \mathbb{L}^{3}-\mathbb{L}^{2}=\mathbb{T}(\mathbb{T}+1)^{2},(\mathbb{T}+1)^{2}, \mathbb{T}(\mathbb{T}+1) | | |
| cardona-qft-methods_FO1922 | 135 | 0.999 | \mathbb{T}(\mathbb{T}+1)^{2} | | |
| cardona-qft-methods_FO1923 | 136 | 1.000 | G \backslash e, G / e | | |
| cardona-qft-methods_FO1924 | 136 | 1.000 | G_{m e} | | |
| cardona-qft-methods_FO1925 | 136 | 1.000 | T_{y} | | |
| cardona-qft-methods_FO1926 | 136 | 1.000 | { }^{\text {Hir95 }} | | |
| cardona-qft-methods_FO1927 | 136 | 1.000 | \mathbb{U}\left(G_{m e}\right) | | |
| cardona-qft-methods_FO1928 | 136 | 1.000 | m \geq 2 | | |
| cardona-qft-methods_FO1929 | 136 | 1.000 | \chi\left(Y_{G / e}\right) | | |
| cardona-qft-methods_FO1930 | 136 | 0.590 | G=\mathrm{a} 2 | | |
| cardona-qft-methods_FO1931 | 136 | 0.590 | \mathbb{U}(G)=\mathbb{T}(\mathbb{T}+1), \mathbb{U}(G \backslash e)=\mathbb{T}+1 | | |
| cardona-qft-methods_FO1932 | 136 | 0.998 | \mathbb{U}(G / e)=\mathbb{T} | | |
| cardona-qft-methods_FO1933 | 136 | 0.998 | G_{m e}= | | |
| cardona-qft-methods_FO1934 | 136 | 1.000 | (m+1) | | |
| cardona-qft-methods_FO1935 | 137 | 1.000 | G / e | | |
| cardona-qft-methods_FO1936 | 137 | 0.998 | \underline{t} \in \mathbb{A}^{n}, n= | | |
| cardona-qft-methods_FO1937 | 137 | 1.000 | \underline{t}^{\prime} | | |
| cardona-qft-methods_FO1938 | 137 | 1.000 | \underline{t}^{\prime} \notin Y_{G \backslash e} | | |
| cardona-qft-methods_FO1939 | 137 | 1.000 | \underline{t}^{\prime} \in Y_{G / e} | | |
| cardona-qft-methods_FO1940 | 137 | 1.000 | \mathbb{L} | | |
| cardona-qft-methods_FO1941 | 137 | 1.000 | e^{\prime} | | |
| cardona-qft-methods_FO1942 | 137 | 0.999 | \left[Y_{G_{2 e} / e} \cup\right. | | |
| cardona-qft-methods_FO1943 | 137 | 0.950 | \left.Y_{G_{2 e} \backslash e}\right] | | |
| cardona-qft-methods_FO1944 | 137 | 0.950 | \left[Y_{G / e} \cup Y_{G \backslash e}\right] | | |
| cardona-qft-methods_FO1945 | 138 | 1.000 | C_{G \backslash e, G / e}(T) | | |
| cardona-qft-methods_FO1946 | 138 | 1.000 | \Psi_{G / e}(T) | | |
| cardona-qft-methods_FO1947 | 138 | 1.000 | \Psi_{G \backslash e} | | |
| cardona-qft-methods_FO1948 | 138 | 0.573 | C_{3-\text { banana }}(T)= | | |
| cardona-qft-methods_FO1949 | 138 | 1.000 | T\left(1+T+T^{2}\right) | | |
| cardona-qft-methods_FO1950 | 139 | 1.000 | m \geq 1 | | |
| cardona-qft-methods_FO1951 | 139 | 1.000 | p \in \mathbb{P}^{n-1} | | |
| cardona-qft-methods_FO1952 | 139 | 1.000 | B \ell_{p} X_{G} | | |
| cardona-qft-methods_FO1953 | 139 | 1.000 | \mathbb{P}^{n-2} | | |
| cardona-qft-methods_FO1954 | 139 | 1.000 | X_{G \backslash e} \cap X_{G / e} | | |
| cardona-qft-methods_FO1955 | 139 | 0.998 | X \times \mathbb{P}^{\ell} | | |
| cardona-qft-methods_FO1956 | 139 | 0.998 | Y \times \mathbb{P}^{m} | | |
| cardona-qft-methods_FO1957 | 139 | 1.000 | \ell, m | | |
| cardona-qft-methods_FO1958 | 140 | 1.000 | X_{1} | | |
| cardona-qft-methods_FO1959 | 140 | 1.000 | X_{2} | | |
| cardona-qft-methods_FO1960 | 140 | 1.000 | Y_{1} | | |
| cardona-qft-methods_FO1961 | 140 | 1.000 | Y_{2} | | |
| cardona-qft-methods_FO1962 | 140 | 1.000 | X_{1} \times Y_{1} | | |
| cardona-qft-methods_FO1963 | 140 | 1.000 | X_{2} \times Y_{2} | | |
| cardona-qft-methods_FO1964 | 140 | 1.000 | \geq 2 | | |
| cardona-qft-methods_FO1965 | 140 | 1.000 | { }^{\text {AKMW02 }} | | |
| cardona-qft-methods_FO1966 | 140 | 0.873 | \left({ }^{\text {LL03 }}\right) | | |
| cardona-qft-methods_FO1967 | 140 | 1.000 | S B | | |
| cardona-qft-methods_FO1968 | 140 | 1.000 | X \times Y | | |
| cardona-qft-methods_FO1969 | 140 | 1.000 | \mathbb{Z}[S B] | | |
| cardona-qft-methods_FO1970 | 140 | 1.000 | [X]_{S B} | | |
| cardona-qft-methods_FO1971 | 140 | 1.000 | [X]_{S B}=1 | | |
| cardona-qft-methods_FO1972 | 141 | 1.000 | \mathbb{P}^{1} \backslash \mathbb{P}^{0} | | |
| cardona-qft-methods_FO1973 | 141 | 1.000 | \left[\mathbb{P}^{1}\right]_{S B}-\left[\mathbb{P}^{0}\right]_{S B}=1-1=0 | | |
| cardona-qft-methods_FO1974 | 141 | 0.922 | \left[\mathbb{P}^{1}\right]_{S B}- | | |
| cardona-qft-methods_FO1975 | 141 | 1.000 | 2\left[\mathbb{P}^{0}\right]_{S B}=-1 | | |
| cardona-qft-methods_FO1976 | 141 | 0.999 | { }^{\text {AM11c }} | | |
| cardona-qft-methods_FO1977 | 141 | 0.999 | { }^{\text {LL03 }} | | |
| cardona-qft-methods_FO1978 | 141 | 0.998 | X \mapsto[X]_{S B} | | |
| cardona-qft-methods_FO1979 | 141 | 0.996 | K_{0}(\operatorname{Var}) \rightarrow \mathbb{Z}[S B] | | |
| cardona-qft-methods_FO1980 | 141 | 1.000 | (\mathbb{L}) | | |
| cardona-qft-methods_FO1981 | 142 | 1.000 | B \times \mathbb{P}^{r} | | |
| cardona-qft-methods_FO1982 | 142 | 1.000 | B \subset X | | |
| cardona-qft-methods_FO1983 | 142 | 1.000 | B \ell_{B} X | | |
| cardona-qft-methods_FO1984 | 142 | 0.903 | ) \rightarrow \mathbb{Z}[S B] | | |
| cardona-qft-methods_FO1985 | 142 | 0.998 | \left[B \ell_{B} X\right] \equiv[X] \operatorname{modulo}(\mathbb{L}) | | |
| cardona-qft-methods_FO1986 | 142 | 1.000 | F \rightarrow \mathbb{Z}[S B] | | |
| cardona-qft-methods_FO1987 | 142 | 1.000 | \left[\hat{Y}_{G}\right]=\mathbb{U}(G) | | |
| cardona-qft-methods_FO1988 | 143 | 1.000 | \mathbb{U}(G) \bmod | | |
| cardona-qft-methods_FO1989 | 143 | 1.000 | \mathbb{Z} \rightarrow \mathbb{Z}[S B] | | |
| cardona-qft-methods_FO1990 | 143 | 0.939 | 15 \mathrm{in}^{\text {BS12 }} | | |
| cardona-qft-methods_FO1991 | 143 | 1.000 | \mathbb{L}^{2} | | |
| cardona-qft-methods_FO1992 | 143 | 0.475 | c+\mathbb{L} \cdot M^{\prime} | | |
| cardona-qft-methods_FO1993 | 143 | 0.475 | c \in \mathbb{Z} | | |
| cardona-qft-methods_FO1994 | 143 | 0.475 | M^{\prime} \in K_{0}(\mathrm{Var}) | | |
| cardona-qft-methods_FO1995 | 143 | 1.000 | h^{p, q} | | |
| cardona-qft-methods_FO1996 | 143 | 1.000 | p=0, q>0 | | |
| cardona-qft-methods_FO1997 | 143 | 1.000 | p>0, q=0 | | |
| cardona-qft-methods_FO1998 | 144 | 1.000 | \mathbb{L}^{n}-1(n>0) | | |
| cardona-qft-methods_FO1999 | 144 | 1.000 | \mathbb{L}^{n}-1 | | |
| cardona-qft-methods_FO2000 | 144 | 1.000 | K\left(\operatorname{Var}_{\mathbb{Z}}\right)_{\mathbb{L}} | | |
| cardona-qft-methods_FO2001 | 144 | 1.000 | \mathbb{Z}[\mathbb{L}]_{\mathbb{L}} | | |
| cardona-qft-methods_FO2002 | 145 | 1.000 | \phi^{4} | | |
| cardona-qft-methods_FO2003 | 149 | 1.000 | { }^{2,3} | | |
| cardona-qft-methods_FO2004 | 149 | 1.000 | { }^{4-6} | | |
| cardona-qft-methods_FO2005 | 149 | 1.000 | S O(D, 1) | | |
| cardona-qft-methods_FO2006 | 149 | 1.000 | S O(D-1,2) | | |
| cardona-qft-methods_FO2007 | 149 | 0.926 | I S O(D-1,1) | | |
| cardona-qft-methods_FO2008 | 149 | 1.000 | 2 p | | |
| cardona-qft-methods_FO2009 | 149 | 1.000 | t_{1}<0 | | |
| cardona-qft-methods_FO2010 | 149 | 1.000 | t_{1} | | |
| cardona-qft-methods_FO2011 | 149 | 0.985 | t_{1} \rightarrow \operatorname{Petya}\left(t_{1}\right) | | |
| cardona-qft-methods_FO2012 | 149 | 0.985 | t_{2}, t_{1}<t_{2} \leq 0 | | |
| cardona-qft-methods_FO2013 | 149 | 1.000 | t_{2} | | |
| cardona-qft-methods_FO2014 | 150 | 1.000 | \mathbb{G} | | |
| cardona-qft-methods_FO2015 | 150 | 1.000 | \forall x \in M, g(x) \in \mathbb{G} | | |
| cardona-qft-methods_FO2016 | 150 | 0.999 | \mathcal{C}(\mathbf{A}) | | |
| cardona-qft-methods_FO2017 | 150 | 0.999 | (2 n+1) | | |
| cardona-qft-methods_FO2018 | 150 | 0.999 | n \geq 0 | | |
| cardona-qft-methods_FO2019 | 150 | 1.000 | A_{\mu} | | |
| cardona-qft-methods_FO2020 | 151 | 1.000 | \partial_{\mu} j^{\mu}=0 | | |
| cardona-qft-methods_FO2021 | 151 | 1.000 | \partial | | |
| cardona-qft-methods_FO2022 | 151 | 0.686 | (\mathbb{G}) | | |
| cardona-qft-methods_FO2023 | 151 | 0.686 | d \Omega | | |
| cardona-qft-methods_FO2024 | 151 | 1.000 | (2 n) | | |
| cardona-qft-methods_FO2025 | 151 | 1.000 | j^{\mu} | | |
| cardona-qft-methods_FO2026 | 151 | 1.000 | \partial M | | |
| cardona-qft-methods_FO2027 | 151 | 1.000 | d \star j=0 | | |
| cardona-qft-methods_FO2028 | 151 | 0.989 | { }^{\text {a }} | | |
| cardona-qft-methods_FO2029 | 151 | 0.989 | \alpha=(p!)^{-1} \alpha_{\mu_{1} \mu_{2} \cdots \mu_{p}} d x^{\mu_{1}} \wedge d x^{\mu 2} \wedge \cdots \wedge d x^{\mu_{p}} | | |
| cardona-qft-methods_FO2030 | 151 | 0.989 | (D-p) | | |
| cardona-qft-methods_FO2031 | 151 | 0.694 | \star \alpha=[p!(D-p)!]^{-1} \epsilon_{\nu_{1} \nu_{2} \cdots \nu_{D-p}}{ }^{\mu_{1} \mu_{2} \cdots \mu_{p}} \alpha_{\mu_{1} \mu_{2} \cdots \mu_{p}} d x^{\nu_{1}} \wedge d x^{\nu 2} \wedge \cdots \wedge d x^{\nu_{D-p}} | | |
| cardona-qft-methods_FO2032 | 152 | 1.000 | \star j | | |
| cardona-qft-methods_FO2033 | 152 | 0.998 | (D-2 n-1) | | |
| cardona-qft-methods_FO2034 | 152 | 1.000 | j= | | |
| cardona-qft-methods_FO2035 | 152 | 1.000 | q \delta(\Gamma) d z | | |
| cardona-qft-methods_FO2036 | 152 | 1.000 | \delta(\Gamma) | | |
| cardona-qft-methods_FO2037 | 152 | 1.000 | 2 n | | |
| cardona-qft-methods_FO2038 | 152 | 1.000 | \mathbf{K}_{a}(a=1,2, \ldots, N) | | |
| cardona-qft-methods_FO2039 | 152 | 1.000 | \mathbf{K}_{a} | | |
| cardona-qft-methods_FO2040 | 152 | 1.000 | g(x)=\exp \left[\alpha^{a}(x) \mathbf{K}_{a}\right] | | |
| cardona-qft-methods_FO2041 | 152 | 1.000 | D=d-\mathbf{A} | | |
| cardona-qft-methods_FO2042 | 152 | 1.000 | \partial_{\mu}-i A_{\mu} | | |
| cardona-qft-methods_FO2043 | 152 | 1.000 | \nabla_{\mu}=\partial_{\mu}+\boldsymbol{\Gamma}_{\mu} | | |
| cardona-qft-methods_FO2044 | 152 | 1.000 | \mathbf{F}=d \mathbf{A}+\mathbf{A} \wedge \mathbf{A} | | |
| cardona-qft-methods_FO2045 | 152 | 1.000 | \vec{E} | | |
| cardona-qft-methods_FO2046 | 152 | 1.000 | \vec{B} | | |
| cardona-qft-methods_FO2047 | 152 | 1.000 | 2 k | | |
| cardona-qft-methods_FO2048 | 153 | 0.993 | \mathbf{A}: M \mapsto \mathbb{L} | | |
| cardona-qft-methods_FO2049 | 153 | 1.000 | P_{2 k}(\mathbf{F})=\left\langle\mathbf{F}^{k}\right\rangle | | |
| cardona-qft-methods_FO2050 | 153 | 1.000 | \langle\cdots\rangle | | |
| cardona-qft-methods_FO2051 | 153 | 0.973 | T r | | |
| cardona-qft-methods_FO2052 | 153 | 0.973 | P_{2 k} | | |
| cardona-qft-methods_FO2053 | 153 | 1.000 | \delta_{\text {gauge }} P_{2 k}=0 | | |
| cardona-qft-methods_FO2054 | 153 | 1.000 | d P_{2 k}=0 | | |
| cardona-qft-methods_FO2055 | 153 | 1.000 | (2 k-1) | | |
| cardona-qft-methods_FO2056 | 153 | 1.000 | P_{2 k}= | | |
| cardona-qft-methods_FO2057 | 153 | 1.000 | d \mathcal{C}_{2 k-1} | | |
| cardona-qft-methods_FO2058 | 153 | 1.000 | \int_{M} P_{2 k}=c_{2 k}(M) \in \mathbf{Z} | | |
| cardona-qft-methods_FO2059 | 153 | 0.988 | \mathbf{F} | | |
| cardona-qft-methods_FO2060 | 153 | 0.988 | D \mathbf{F}=d \mathbf{F}+[\mathbf{A}, \mathbf{F}] \equiv 0 | | |
| cardona-qft-methods_FO2061 | 153 | 1.000 | d \phi=0 | | |
| cardona-qft-methods_FO2062 | 153 | 0.996 | \phi=d | | |
| cardona-qft-methods_FO2063 | 153 | 1.000 | \mathcal{C}_{2 n-1} | | |
| cardona-qft-methods_FO2064 | 153 | 0.991 | d \mathbf{A} | | |
| cardona-qft-methods_FO2065 | 153 | 0.993 | \operatorname{Tr}\left[\mathbf{F}^{k}\right] | | |
| cardona-qft-methods_FO2066 | 154 | 1.000 | \mathcal{C}_{2 k-1} | | |
| cardona-qft-methods_FO2067 | 154 | 1.000 | (2 n-1) | | |
| cardona-qft-methods_FO2068 | 154 | 1.000 | M^{2 n-1} | | |
| cardona-qft-methods_FO2069 | 155 | 1.000 | \xi^{\mu} | | |
| cardona-qft-methods_FO2070 | 155 | 0.999 | v^{\prime \mu} | | |
| cardona-qft-methods_FO2071 | 155 | 0.999 | x^{\prime} | | |
| cardona-qft-methods_FO2072 | 156 | 1.000 | \mathcal{H}_{\mu} | | |
| cardona-qft-methods_FO2073 | 156 | 1.000 | g^{i j}(x) | | |
| cardona-qft-methods_FO2074 | 156 | 1.000 | x, \mathcal{H}_{\perp} | | |
| cardona-qft-methods_FO2075 | 156 | 1.000 | x^{\perp}, \mathcal{H}_{i} | | |
| cardona-qft-methods_FO2076 | 156 | 1.000 | x^{i} ; \delta(x, y) | | |
| cardona-qft-methods_FO2077 | 156 | 0.965 | x=y | | |
| cardona-qft-methods_FO2078 | 156 | 0.965 | \delta(x, y),{ }_{i}=\left(\partial / \partial y^{i}\right) \delta(x, y) | | |
| cardona-qft-methods_FO2079 | 157 | 0.999 | S O(3,1) | | |
| cardona-qft-methods_FO2080 | 158 | 0.833 | \mathbb{G} \supseteq S O(3,1) | | |
| cardona-qft-methods_FO2081 | 158 | 0.833 | (S O(4,1)) | | |
| cardona-qft-methods_FO2082 | 158 | 0.855 | (S O(3,2)) | | |
| cardona-qft-methods_FO2083 | 158 | 0.855 | (S O(4,2)) | | |
| cardona-qft-methods_FO2084 | 158 | 0.855 | I S O(3,1)) | | |
| cardona-qft-methods_FO2085 | 158 | 1.000 | S O(D-1,1) | | |
| cardona-qft-methods_FO2086 | 158 | 1.000 | d^{2} \equiv 0 | | |
| cardona-qft-methods_FO2087 | 158 | 1.000 | e_{\mu}^{a}(x) | | |
| cardona-qft-methods_FO2088 | 158 | 0.615 | \omega^{a}{ }_{b \mu}(x) | | |
| cardona-qft-methods_FO2089 | 159 | 1.000 | (-1,1,1, \cdots, 1) | | |
| cardona-qft-methods_FO2090 | 159 | 1.000 | T_{x} | | |
| cardona-qft-methods_FO2091 | 159 | 1.000 | \left\{T_{x}, x \in M\right\} | | |
| cardona-qft-methods_FO2092 | 159 | 1.000 | d x^{\mu} | | |
| cardona-qft-methods_FO2093 | 159 | 1.000 | z^{a} | | |
| cardona-qft-methods_FO2094 | 159 | 1.000 | \eta_{a b} | | |
| cardona-qft-methods_FO2095 | 159 | 1.000 | e_{\mu}^{a} | | |
| cardona-qft-methods_FO2096 | 160 | 1.000 | T_{x}, S O(D-1,1) | | |
| cardona-qft-methods_FO2097 | 160 | 1.000 | \boldsymbol{\Lambda}(x) | | |
| cardona-qft-methods_FO2098 | 160 | 1.000 | D(D+1) / 2 | | |
| cardona-qft-methods_FO2099 | 160 | 1.000 | D(D-1) / 2 | | |
| cardona-qft-methods_FO2100 | 160 | 1.000 | e^{a}(x)=e_{\mu}^{a}(x) d x^{\mu} | | |
| cardona-qft-methods_FO2101 | 160 | 1.000 | \Lambda(x) | | |
| cardona-qft-methods_FO2102 | 160 | 0.955 | { }^{\mathrm{d}} | | |
| cardona-qft-methods_FO2103 | 160 | 1.000 | T_{x+d x} | | |
| cardona-qft-methods_FO2104 | 160 | 1.000 | \phi^{a}(x) | | |
| cardona-qft-methods_FO2105 | 160 | 1.000 | x+d x | | |
| cardona-qft-methods_FO2106 | 160 | 1.000 | { }^{2,7,16} | | |
| cardona-qft-methods_FO2107 | 161 | 0.979 | \phi^{a} | | |
| cardona-qft-methods_FO2108 | 161 | 0.979 | \phi_{\|}^{a} | | |
| cardona-qft-methods_FO2109 | 161 | 0.993 | \omega_{b \mu}^{a} | | |
| cardona-qft-methods_FO2110 | 161 | 0.993 | \Gamma_{\lambda \rho}^{\mu} | | |
| cardona-qft-methods_FO2111 | 161 | 1.000 | \omega^{a}{ }_{b}=\omega^{a}{ }_{b \mu} d x^{\mu} | | |
| cardona-qft-methods_FO2112 | 161 | 1.000 | \epsilon_{a_{1} a_{2} \cdots a_{D}} | | |
| cardona-qft-methods_FO2113 | 161 | 1.000 | \left(\partial_{\mu} \eta_{a b}=0, \partial_{\mu} \epsilon_{a_{1} a_{2} \cdots a_{D}}=0\right) | | |
| cardona-qft-methods_FO2114 | 162 | 1.000 | \omega^{a b}=-\omega^{b a} | | |
| cardona-qft-methods_FO2115 | 162 | 0.977 | D^{2}(D-1) / 2 | | |
| cardona-qft-methods_FO2116 | 162 | 0.968 | \left(D^{2}(D+1) / 2\right) | | |
| cardona-qft-methods_FO2117 | 162 | 1.000 | d x^{\mu} \partial_{\mu} \wedge | | |
| cardona-qft-methods_FO2118 | 162 | 0.468 | \alpha_{p} | | |
| cardona-qft-methods_FO2119 | 162 | 0.468 | d \alpha_{p} | | |
| cardona-qft-methods_FO2120 | 162 | 1.000 | { }^{16,17} | | |
| cardona-qft-methods_FO2121 | 162 | 0.924 | R^{a}{ }_{b} | | |
| cardona-qft-methods_FO2122 | 162 | 0.788 | \omega^{a}{ }_{b}(x) | | |
| cardona-qft-methods_FO2123 | 162 | 0.788 | A^{a}{ }_{b}= | | |
| cardona-qft-methods_FO2124 | 162 | 0.955 | A^{a}{ }_{b \mu} d x^{\mu} | | |
| cardona-qft-methods_FO2125 | 162 | 0.953 | R_{b}^{a} | | |
| cardona-qft-methods_FO2126 | 162 | 1.000 | R^{\alpha \beta}{ }_{\mu \nu} | | |
| cardona-qft-methods_FO2127 | 163 | 1.000 | e^{a} | | |
| cardona-qft-methods_FO2128 | 163 | 1.000 | T^{a} | | |
| cardona-qft-methods_FO2129 | 163 | 0.999 | \bar{\omega} | | |
| cardona-qft-methods_FO2130 | 163 | 0.999 | \kappa | | |
| cardona-qft-methods_FO2131 | 163 | 1.000 | \bar{R}_{b}^{a} | | |
| cardona-qft-methods_FO2132 | 163 | 1.000 | \bar{D} | | |
| cardona-qft-methods_FO2133 | 164 | 0.896 | \omega^{a}{ }_{b \mu} | | |
| cardona-qft-methods_FO2134 | 164 | 1.000 | R^{a b} | | |
| cardona-qft-methods_FO2135 | 164 | 1.000 | e^{a}, \omega^{a b} | | |
| cardona-qft-methods_FO2136 | 164 | 0.793 | \omega_{b}^{a} | | |
| cardona-qft-methods_FO2137 | 164 | 0.793 | R_{b}^{a}, T^{a} | | |
| cardona-qft-methods_FO2138 | 164 | 0.508 | I[e, \omega] | | |
| cardona-qft-methods_FO2139 | 164 | 0.508 | \omega^{a}{ }_{b} | | |
| cardona-qft-methods_FO2140 | 164 | 0.852 | \mu, \nu | | |
| cardona-qft-methods_FO2141 | 165 | 0.666 | e^{a}, \omega^{a}{ }_{b} | | |
| cardona-qft-methods_FO2142 | 165 | 1.000 | \epsilon_{a_{1} \cdots a_{D}} | | |
| cardona-qft-methods_FO2143 | 165 | 1.000 | { }^{\mathrm{e}} R_{\mu \nu}=E_{a}^{\lambda} \eta_{b c} e_{\mu}^{c} R_{\lambda \nu}^{a b} | | |
| cardona-qft-methods_FO2144 | 165 | 1.000 | R_{\alpha \beta} R_{\mu \nu} R^{\alpha \mu \beta \nu} | | |
| cardona-qft-methods_FO2145 | 165 | 0.988 | e^{a}, R_{b}^{a}, T^{a} | | |
| cardona-qft-methods_FO2146 | 165 | 1.000 | \mathbf{P}_{2 k} | | |
| cardona-qft-methods_FO2147 | 165 | 1.000 | \mathbf{E}_{2 n} | | |
| cardona-qft-methods_FO2148 | 165 | 1.000 | 4 k | | |
| cardona-qft-methods_FO2149 | 165 | 0.774 | { }^{\mathrm{e}} | | |
| cardona-qft-methods_FO2150 | 165 | 0.774 | E_{a}^{\lambda} | | |
| cardona-qft-methods_FO2151 | 165 | 0.774 | E_{a}^{\lambda} e^{b}{ }_{\lambda}=\delta_{b}^{a} | | |
| cardona-qft-methods_FO2152 | 166 | 1.000 | \Omega_{n} | | |
| cardona-qft-methods_FO2153 | 166 | 1.000 | \tilde{\Omega}_{k} | | |
| cardona-qft-methods_FO2154 | 166 | 1.000 | D=2 n | | |
| cardona-qft-methods_FO2155 | 166 | 1.000 | 4\left(k_{1}+k_{2}+\cdots+k_{r}\right)=D | | |
| cardona-qft-methods_FO2156 | 166 | 1.000 | D / 4 | | |
| cardona-qft-methods_FO2157 | 166 | 0.994 | { }^{\mathrm{f}} | | |
| cardona-qft-methods_FO2158 | 166 | 1.000 | \tau_{k}, \zeta_{k} | | |
| cardona-qft-methods_FO2159 | 166 | 1.000 | v_{k} | | |
| cardona-qft-methods_FO2160 | 166 | 1.000 | R^{a}{ }_{b} e^{b} | | |
| cardona-qft-methods_FO2161 | 166 | 1.000 | a_{p} | | |
| cardona-qft-methods_FO2162 | 166 | 1.000 | L_{p}^{D} | | |
| cardona-qft-methods_FO2163 | 166 | 1.000 | L_{D / 2}^{D}=\mathcal{E}_{D} | | |
| cardona-qft-methods_FO2164 | 166 | 1.000 | p(D / 4) \sim \frac{1}{\sqrt{3} D} \exp [\pi \sqrt{D / 6}] | | |
| cardona-qft-methods_FO2165 | 167 | 0.994 | D=2 | | |
| cardona-qft-methods_FO2166 | 167 | 1.000 | V_{2}=0 | | |
| cardona-qft-methods_FO2167 | 167 | 1.000 | I_{2} | | |
| cardona-qft-methods_FO2168 | 167 | 0.998 | D=3 | | |
| cardona-qft-methods_FO2169 | 167 | 0.998 | D=4 | | |
| cardona-qft-methods_FO2170 | 167 | 1.000 | \mathbf{E}_{4} | | |
| cardona-qft-methods_FO2171 | 167 | 1.000 | D=5 | | |
| cardona-qft-methods_FO2172 | 167 | 1.000 | D(D-3) / 2 | | |
| cardona-qft-methods_FO2173 | 168 | 1.000 | { }^{\mathrm{g}} | | |
| cardona-qft-methods_FO2174 | 168 | 1.000 | { }^{12,23} | | |
| cardona-qft-methods_FO2175 | 168 | 1.000 | k^{-2} | | |
| cardona-qft-methods_FO2176 | 168 | 1.000 | k^{-2}+k^{-4} | | |
| cardona-qft-methods_FO2177 | 168 | 1.000 | \omega^{a b} | | |
| cardona-qft-methods_FO2178 | 168 | 1.000 | I_{D} | | |
| cardona-qft-methods_FO2179 | 168 | 1.000 | \mathcal{E}_{a} | | |
| cardona-qft-methods_FO2180 | 168 | 1.000 | \mathcal{E}_{a b} | | |
| cardona-qft-methods_FO2181 | 168 | 1.000 | d^{2}=0 | | |
| cardona-qft-methods_FO2182 | 168 | 0.826 | \left(E_{a}^{\mu}\right) | | |
| cardona-qft-methods_FO2183 | 168 | 1.000 | \Gamma_{\mu \nu}^{\lambda} | | |
| cardona-qft-methods_FO2184 | 168 | 1.000 | \mu \nu | | |
| cardona-qft-methods_FO2185 | 169 | 1.000 | g_{\mu \nu} | | |
| cardona-qft-methods_FO2186 | 169 | 1.000 | f(R) | | |
| cardona-qft-methods_FO2187 | 169 | 1.000 | D \leq 4 | | |
| cardona-qft-methods_FO2188 | 169 | 1.000 | D>4 | | |
| cardona-qft-methods_FO2189 | 169 | 1.000 | (15,16) | | |
| cardona-qft-methods_FO2190 | 170 | 1.000 | I[\omega, e]=I[\omega(e, \partial e), e] | | |
| cardona-qft-methods_FO2191 | 170 | 1.000 | \omega(e, \partial e) | | |
| cardona-qft-methods_FO2192 | 170 | 0.857 | T^{a}=0 .{ }^{18} | | |
| cardona-qft-methods_FO2193 | 170 | 1.000 | \mathbf{P}_{4} v_{1} \tau_{0} \zeta_{0} | | |
| cardona-qft-methods_FO2194 | 170 | 0.964 | S O(5) | | |
| cardona-qft-methods_FO2195 | 170 | 0.964 | S O(4) | | |
| cardona-qft-methods_FO2196 | 170 | 0.948 | S O(n, 5-n | | |
| cardona-qft-methods_FO2197 | 170 | 0.948 | S O(m, 4-m)) .^{28} | | |
| cardona-qft-methods_FO2198 | 171 | 1.000 | \mathbf{P}_{4} | | |
| cardona-qft-methods_FO2199 | 171 | 1.000 | \mathbf{N}_{4} | | |
| cardona-qft-methods_FO2200 | 171 | 0.982 | S O(2,1) | | |
| cardona-qft-methods_FO2201 | 171 | 1.000 | 4 k-1 | | |
| cardona-qft-methods_FO2202 | 171 | 1.000 | D=7 | | |
| cardona-qft-methods_FO2203 | 172 | 1.000 | v, \tau | | |
| cardona-qft-methods_FO2204 | 172 | 0.999 | { }^{-2} | | |
| cardona-qft-methods_FO2205 | 173 | 1.000 | (\kappa) | | |
| cardona-qft-methods_FO2206 | 173 | 1.000 | l^{D-2 p} | | |
| cardona-qft-methods_FO2207 | 173 | 1.000 | \left[e^{a}\right]=l | | |
| cardona-qft-methods_FO2208 | 173 | 1.000 | \left[\omega^{a b}\right]=l^{0} | | |
| cardona-qft-methods_FO2209 | 173 | 1.000 | \hat{\omega}^{a b}=\omega^{a b}+\xi \epsilon^{a b c} e_{c} | | |
| cardona-qft-methods_FO2210 | 173 | 1.000 | \lambda^{a}{ }_{b} | | |
| cardona-qft-methods_FO2211 | 174 | 1.000 | e^{c}, R^{a b} | | |
| cardona-qft-methods_FO2212 | 174 | 1.000 | \epsilon_{a b c} | | |
| cardona-qft-methods_FO2213 | 174 | 1.000 | L_{3} | | |
| cardona-qft-methods_FO2214 | 174 | 0.531 | { }^{\mathrm{h}} | | |
| cardona-qft-methods_FO2215 | 174 | 1.000 | \lambda^{a} | | |
| cardona-qft-methods_FO2216 | 174 | 1.000 | \delta e | | |
| cardona-qft-methods_FO2217 | 174 | 1.000 | \delta \omega | | |
| cardona-qft-methods_FO2218 | 177 | 0.658 | 2+1 | | |
| cardona-qft-methods_FO2219 | 174 | 1.000 | \Lambda=\mp l^{-2} | | |
| cardona-qft-methods_FO2220 | 175 | 1.000 | \Lambda \neq 0 | | |
| cardona-qft-methods_FO2221 | 175 | 1.000 | \Lambda>0 | | |
| cardona-qft-methods_FO2222 | 175 | 1.000 | \Lambda<0 | | |
| cardona-qft-methods_FO2223 | 175 | 0.995 | W^{A B} | | |
| cardona-qft-methods_FO2224 | 175 | 0.995 | \Lambda^{A B} | | |
| cardona-qft-methods_FO2225 | 175 | 0.999 | a, b, . .=1,2, . . D | | |
| cardona-qft-methods_FO2226 | 175 | 0.999 | A, B, \ldots=1,2, . ., D+1 | | |
| cardona-qft-methods_FO2227 | 175 | 1.000 | \Lambda^{A B}=-\Lambda^{B A} | | |
| cardona-qft-methods_FO2228 | 175 | 0.957 | S O(r, s) | | |
| cardona-qft-methods_FO2229 | 176 | 1.000 | \Upsilon^{A B} | | |
| cardona-qft-methods_FO2230 | 176 | 1.000 | W^{A B}=\Upsilon^{B C} W_{C}^{A} | | |
| cardona-qft-methods_FO2231 | 176 | 1.000 | W^{A B}+W^{B A}=0 | | |
| cardona-qft-methods_FO2232 | 176 | 1.000 | \omega^{a b}+\omega^{b a}= | | |
| cardona-qft-methods_FO2233 | 176 | 0.957 | \omega^{a b} \equiv \eta^{b c} \omega^{a}{ }_{c} | | |
| cardona-qft-methods_FO2234 | 176 | 0.940 | l \rightarrow \infty(\lambda \rightarrow 0) | | |
| cardona-qft-methods_FO2235 | 176 | 0.940 | (7,8) | | |
| cardona-qft-methods_FO2236 | 176 | 0.516 | (c \rightarrow | | |
| cardona-qft-methods_FO2237 | 176 | 0.788 | \infty | | |
| cardona-qft-methods_FO2238 | 176 | 1.000 | { }^{31,32} | | |
| cardona-qft-methods_FO2239 | 176 | 1.000 | l | | |
| cardona-qft-methods_FO2240 | 176 | 1.000 | l \rightarrow \infty | | |
| cardona-qft-methods_FO2241 | 177 | 1.000 | \geq 3 | | |
| cardona-qft-methods_FO2242 | 177 | 0.999 | S O(D, 1), S O(D-1,2), I S O(D-1,1) | | |
| cardona-qft-methods_FO2243 | 177 | 1.000 | D=2 n-1 | | |
| cardona-qft-methods_FO2244 | 177 | 0.995 | S O(2 n-2,2), S O(2 n-1,1) | | |
| cardona-qft-methods_FO2245 | 177 | 0.995 | I S O(2 n-2,1) | | |
| cardona-qft-methods_FO2246 | 177 | 0.994 | S O(3,1), S O(2,2) | | |
| cardona-qft-methods_FO2247 | 177 | 0.994 | I S O(2,1) | | |
| cardona-qft-methods_FO2248 | 178 | 1.000 | T^{a}=0 | | |
| cardona-qft-methods_FO2249 | 178 | 0.991 | (l \rightarrow \infty) | | |
| cardona-qft-methods_FO2250 | 178 | 0.757 | a, b | | |
| cardona-qft-methods_FO2251 | 178 | 0.757 | A, B | | |
| cardona-qft-methods_FO2252 | 178 | 0.998 | \epsilon_{A B C D} | | |
| cardona-qft-methods_FO2253 | 179 | 1.000 | { }^{\mathrm{i}} | | |
| cardona-qft-methods_FO2254 | 179 | 1.000 | \Upsilon^{A B}=\operatorname{diag} | | |
| cardona-qft-methods_FO2255 | 179 | 0.998 | \left(\eta^{a b}, \mp 1\right) | | |
| cardona-qft-methods_FO2256 | 179 | 0.998 | R^{a b}, T^{a} | | |
| cardona-qft-methods_FO2257 | 179 | 0.997 | (\mathrm{A}) \mathrm{dS}_{3} | | |
| cardona-qft-methods_FO2258 | 179 | 0.936 | \delta L_{3}^{A d S}=d \Omega | | |
| cardona-qft-methods_FO2259 | 179 | 1.000 | 2 n-1 | | |
| cardona-qft-methods_FO2260 | 179 | 1.000 | { }^{\mathrm{j}} | | |
| cardona-qft-methods_FO2261 | 179 | 1.000 | L_{2 n-1} | | |
| cardona-qft-methods_FO2262 | 179 | 1.000 | { }^{36,37} | | |
| cardona-qft-methods_FO2263 | 179 | 1.000 | { }^{38,39} | | |
| cardona-qft-methods_FO2264 | 180 | 1.000 | \bar{\alpha}_{p} | | |
| cardona-qft-methods_FO2265 | 180 | 1.000 | R_{t}^{a b}:=R^{a b}+\left(t^{2} / l^{2}\right) e^{a} e^{b} | | |
| cardona-qft-methods_FO2266 | 180 | 1.000 | a_{3} | | |
| cardona-qft-methods_FO2267 | 180 | 1.000 | \cdots a_{2 n-1} | | |
| cardona-qft-methods_FO2268 | 180 | 1.000 | d L_{2 n-1}^{(A) d S}=\mathbf{E}_{2 n} | | |
| cardona-qft-methods_FO2269 | 181 | 1.000 | { }^{2,41} | | |
| cardona-qft-methods_FO2272 | 181 | 0.999 | S O(2,2) | | |
| cardona-qft-methods_FO2281 | 181 | 0.589 | S U(N) | | |
| cardona-qft-methods_FO2282 | 181 | 0.951 | R, F | | |
| cardona-qft-methods_FO2283 | 181 | 0.951 | \omega_{b}^{a}, A | | |
| cardona-qft-methods_FO2284 | 181 | 0.951 | \mathbf{A} | | |
| cardona-qft-methods_FO2285 | 181 | 1.000 | d L_{3}^{A d S} | | |
| cardona-qft-methods_FO2286 | 182 | 1.000 | L_{3}^{\text {Exotic }} | | |
| cardona-qft-methods_FO2287 | 182 | 1.000 | R^{a b} T_{a} e_{b} | | |
| cardona-qft-methods_FO2295 | 182 | 1.000 | O(D-n, n) | | |
| cardona-qft-methods_FO2296 | 182 | 1.000 | (g) | | |
| cardona-qft-methods_FO2297 | 182 | 1.000 | \chi=2-2 g | | |
| cardona-qft-methods_FO2298 | 182 | 1.000 | S O(D+1) | | |
| cardona-qft-methods_FO2299 | 182 | 1.000 | S O(D) | | |
| cardona-qft-methods_FO2300 | 183 | 1.000 | \Omega^{\prime} | | |
| cardona-qft-methods_FO2301 | 183 | 1.000 | \Omega^{\prime} \rightarrow \widetilde{\Omega}^{\prime}=-\Omega^{\prime} | | |
| cardona-qft-methods_FO2302 | 183 | 1.000 | \int_{\Omega^{\prime}} \rightarrow-\int_{\widetilde{\Omega}^{\prime}} | | |
| cardona-qft-methods_FO2303 | 183 | 1.000 | \widetilde{\Omega}^{\prime} | | |
| cardona-qft-methods_FO2304 | 183 | 0.955 | \chi\left[\Omega \cup \widetilde{\Omega^{\prime}}\right] | | |
| cardona-qft-methods_FO2305 | 183 | 1.000 | D=2 n+1 | | |
| cardona-qft-methods_FO2306 | 184 | 0.979 | R^{a b}=\frac{1}{l^{2}} e^{a} e^{b} | | |
| cardona-qft-methods_FO2307 | 184 | 0.840 | { }^{\text {k }} | | |
| cardona-qft-methods_FO2308 | 184 | 1.000 | A d S / K | | |
| cardona-qft-methods_FO2309 | 184 | 0.793 | \alpha_{p} \mathrm{~s} | | |
| cardona-qft-methods_FO2310 | 184 | 1.000 | { }^{38,39,42} | | |
| cardona-qft-methods_FO2311 | 184 | 1.000 | M^{a b} | | |
| cardona-qft-methods_FO2312 | 184 | 0.995 | { }^{\mathrm{k}} | | |
| cardona-qft-methods_FO2313 | 184 | 0.995 | S O(D, 2) / S O(D-1,1) | | |
| cardona-qft-methods_FO2314 | 184 | 1.000 | S O(D, 2) | | |
| cardona-qft-methods_FO2315 | 185 | 1.000 | L_{2 n}^{B I} | | |
| cardona-qft-methods_FO2316 | 185 | 1.000 | \sqrt{\operatorname{det}\left[R^{a b}+\frac{1}{l^{2}} e^{a} e^{b}\right]} | | |
| cardona-qft-methods_FO2317 | 185 | 1.000 | L_{E M}^{B I}=\sqrt{\operatorname{det}\left[F_{\mu \nu}-\lambda \eta_{\mu \nu}\right]} | | |
| cardona-qft-methods_FO2318 | 185 | 1.000 | { }^{45,46} | | |
| cardona-qft-methods_FO2319 | 185 | 1.000 | R^{a b}+\frac{1}{l^{2}} e^{a} e^{b}=0 | | |
| cardona-qft-methods_FO2320 | 186 | 1.000 | I\left[\phi^{r}\right] | | |
| cardona-qft-methods_FO2321 | 186 | 1.000 | \Theta=0 | | |
| cardona-qft-methods_FO2322 | 186 | 1.000 | B\left(\left.\phi^{r}\right|_{\partial M}\right) | | |
| cardona-qft-methods_FO2323 | 187 | 0.901 | \left(\epsilon_{a b c \ldots} \rightarrow \epsilon\right. | | |
| cardona-qft-methods_FO2324 | 187 | 0.901 | \widetilde{R} | | |
| cardona-qft-methods_FO2325 | 188 | 1.000 | \bar{A} | | |
| cardona-qft-methods_FO2326 | 188 | 1.000 | \mathcal{B}_{2 n} | | |
| cardona-qft-methods_FO2327 | 188 | 0.892 | (\bar{A}) | | |
| cardona-qft-methods_FO2328 | 189 | 1.000 | \mathcal{B}_{2 n}(A, \bar{A}) | | |
| cardona-qft-methods_FO2329 | 189 | 1.000 | \mathcal{C}(\bar{A}) | | |
| cardona-qft-methods_FO2330 | 189 | 1.000 | \bar{M} | | |
| cardona-qft-methods_FO2331 | 189 | 1.000 | \partial M=-\partial \bar{M} | | |
| cardona-qft-methods_FO2332 | 189 | 0.998 | (M) | | |
| cardona-qft-methods_FO2333 | 190 | 1.000 | { }^{9,52} | | |
| cardona-qft-methods_FO2334 | 190 | 1.000 | { }^{53-55} | | |
| cardona-qft-methods_FO2335 | 190 | 1.000 | A_{\mu_{1} \mu_{2} \cdots \mu_{p}} j^{\mu_{1} \mu_{2} \cdots \mu_{p}} | | |
| cardona-qft-methods_FO2336 | 190 | 1.000 | I_{\text {Int }} | | |
| cardona-qft-methods_FO2337 | 190 | 1.000 | j^{\prime \mu}=j^{\mu} | | |
| cardona-qft-methods_FO2338 | 191 | 0.999 | \sqrt{|g|} | | |
| cardona-qft-methods_FO2339 | 191 | 1.000 | j=q * \delta(\Gamma) | | |
| cardona-qft-methods_FO2340 | 191 | 1.000 | A_{\mu} j^{\mu} d^{4} x= | | |
| cardona-qft-methods_FO2341 | 191 | 1.000 | q A \wedge \delta(\Gamma) | | |
| cardona-qft-methods_FO2342 | 191 | 1.000 | z^{\mu} | | |
| cardona-qft-methods_FO2343 | 191 | 0.484 | (2 p+1) | | |
| cardona-qft-methods_FO2344 | 192 | 0.881 | \mathfrak{C}_{2 p+1} | | |
| cardona-qft-methods_FO2345 | 192 | 1.000 | \mathcal{C}_{2 p+1}(\mathbf{A})=\left\langle\mathfrak{C}_{2 p+1}(\mathbf{A})\right\rangle | | |
| cardona-qft-methods_FO2346 | 192 | 0.852 | D-2 p-1 | | |
| cardona-qft-methods_FO2347 | 192 | 0.852 | \mathbf{j} | | |
| cardona-qft-methods_FO2348 | 192 | 1.000 | d x^{\alpha_{i}} | | |
| cardona-qft-methods_FO2349 | 192 | 1.000 | I[\mathbf{A} ; \mathbf{j}] | | |
| cardona-qft-methods_FO2350 | 192 | 1.000 | \mathbf{j}_{2 p} | | |
| cardona-qft-methods_FO2351 | 192 | 0.999 | j^{a_{1} a_{2} \cdots a_{s}} \mathbf{K}_{a_{1}} \mathbf{K}_{a_{2}} \cdots \mathbf{K}_{a_{s}} | | |
| cardona-qft-methods_FO2352 | 192 | 0.737 | \mathrm{AdS}_{3} | | |
| cardona-qft-methods_FO2353 | 193 | 1.000 | { }^{62,63} | | |
| cardona-qft-methods_FO2354 | 193 | 0.531 | (2+1) | | |
| cardona-qft-methods_FO2355 | 193 | 1.000 | \theta_{1} | | |
| cardona-qft-methods_FO2356 | 193 | 1.000 | \tilde{M} \subset M | | |
| cardona-qft-methods_FO2357 | 193 | 1.000 | \theta_{2} | | |
| cardona-qft-methods_FO2358 | 193 | 1.000 | j=d \Theta=\left(\theta_{1}-\theta_{2}\right) \delta(\Sigma) d z | | |
| cardona-qft-methods_FO2359 | 193 | 1.000 | \tilde{M}, \Sigma=\partial \tilde{M} | | |
| cardona-qft-methods_FO2360 | 193 | 1.000 | \tilde{M} | | |
| cardona-qft-methods_FO2361 | 193 | 0.934 | \theta \neq 0 .{ }^{65} | | |
| cardona-qft-methods_FO2362 | 200 | 1.000 | { }^{12,33,35,36,46} | | |
| cardona-qft-methods_FO2363 | 201 | 0.996 | S U(3) | | |
| cardona-qft-methods_FO2364 | 202 | 1.000 | S=S_{E H}+S_{S M} | | |
| cardona-qft-methods_FO2365 | 202 | 1.000 | S_{S M} | | |
| cardona-qft-methods_FO2366 | 202 | 1.000 | f\left(R, R^{\mu \nu}, C_{\lambda \mu \nu \kappa}\right) | | |
| cardona-qft-methods_FO2367 | 203 | 1.000 | C^{\infty}(X) | | |
| cardona-qft-methods_FO2368 | 204 | 1.000 | (\mathcal{A}, \mathcal{H}, D) | | |
| cardona-qft-methods_FO2369 | 204 | 1.000 | \pi: \mathcal{A} \rightarrow \mathcal{L}(\mathcal{H}) | | |
| cardona-qft-methods_FO2370 | 204 | 1.000 | \mathcal{L}(\mathcal{H}) | | |
| cardona-qft-methods_FO2371 | 204 | 1.000 | D=D^{*} | | |
| cardona-qft-methods_FO2372 | 204 | 1.000 | \left(1+D^{2}\right)^{-1 / 2} | | |
| cardona-qft-methods_FO2373 | 204 | 1.000 | \mathcal{K} | | |
| cardona-qft-methods_FO2374 | 204 | 0.999 | [a, D] | | |
| cardona-qft-methods_FO2375 | 204 | 1.000 | \mathbb{Z} / 2 | | |
| cardona-qft-methods_FO2376 | 204 | 0.895 | \left(C^{\infty}(M), L^{2}(M, S), \neq_{M}\right) | | |
| cardona-qft-methods_FO2377 | 204 | 1.000 | L^{2}(M, S) | | |
| cardona-qft-methods_FO2378 | 204 | 1.000 | D=\partial_{M} | | |
| cardona-qft-methods_FO2379 | 204 | 0.997 | \gamma_{5} | | |
| cardona-qft-methods_FO2380 | 204 | 1.000 | { }^{22,31,49} | | |
| cardona-qft-methods_FO2381 | 205 | 1.000 | n \in \mathbb{Z} / 8 \mathbb{Z} | | |
| cardona-qft-methods_FO2382 | 205 | 1.000 | \epsilon, \epsilon^{\prime}, \epsilon^{\prime \prime} \in\{ \pm 1\} | | |
| cardona-qft-methods_FO2383 | 264 | 1.000 | \varepsilon | | |
| cardona-qft-methods_FO2386 | 205 | 0.999 | \left[a, b^{0}\right]=0 | | |
| cardona-qft-methods_FO2387 | 205 | 0.999 | a, b \in \mathcal{A} | | |
| cardona-qft-methods_FO2388 | 205 | 0.999 | b^{0} | | |
| cardona-qft-methods_FO2389 | 205 | 0.999 | b^{0}= | | |
| cardona-qft-methods_FO2390 | 205 | 1.000 | J b^{*} J^{-1} | | |
| cardona-qft-methods_FO2391 | 205 | 1.000 | b \in \mathcal{A} | | |
| cardona-qft-methods_FO2392 | 206 | 1.000 | { }^{5,9} | | |
| cardona-qft-methods_FO2393 | 206 | 1.000 | F= | | |
| cardona-qft-methods_FO2394 | 206 | 0.986 | \left(\mathcal{A}_{F}, \mathcal{H}_{F}, D_{F}\right) | | |
| cardona-qft-methods_FO2395 | 206 | 0.986 | A_{F} | | |
| cardona-qft-methods_FO2396 | 206 | 1.000 | F=\left(\mathcal{A}_{F}, \mathcal{H}_{F}, D_{F}\right) | | |
| cardona-qft-methods_FO2397 | 206 | 1.000 | \mathbb{K}_{i}=\mathbb{R} | | |
| cardona-qft-methods_FO2398 | 206 | 1.000 | \mathbb{H} | | |
| cardona-qft-methods_FO2399 | 206 | 1.000 | \mathcal{H}_{F} | | |
| cardona-qft-methods_FO2400 | 207 | 1.000 | D^{*}=D | | |
| cardona-qft-methods_FO2401 | 207 | 0.957 | \left[[D, a], b^{0}\right]=0 | | |
| cardona-qft-methods_FO2402 | 207 | 0.992 | \left(\mathcal{A}_{F}, \mathcal{H}_{F}\right) | | |
| cardona-qft-methods_FO2403 | 207 | 1.000 | \left(\lambda, q_{L}, q_{R}, m\right) \mapsto\left(\bar{\lambda}, \bar{q}_{L}, \bar{q}_{R}, m^{*}\right) | | |
| cardona-qft-methods_FO2404 | 207 | 1.000 | \mathbb{C} \oplus M_{3}(\mathbb{C}) | | |
| cardona-qft-methods_FO2405 | 207 | 1.000 | \mathbb{H}_{L} \oplus \mathbb{H}_{R} | | |
| cardona-qft-methods_FO2406 | 208 | 0.651 | s=(1,-1,-1,1) | | |
| cardona-qft-methods_FO2407 | 208 | 0.651 | A d(s)=-1 | | |
| cardona-qft-methods_FO2408 | 208 | 1.000 | \mathcal{B}= | | |
| cardona-qft-methods_FO2409 | 208 | 0.990 | \left(\mathcal{A}_{L R} \otimes_{\mathbb{R}} \mathcal{A}_{L R}^{o p}\right)_{p} | | |
| cardona-qft-methods_FO2410 | 208 | 0.990 | p=\frac{1}{2}\left(1-s \otimes s^{0}\right) | | |
| cardona-qft-methods_FO2411 | 208 | 0.990 | \mathcal{A}^{0}=\mathcal{A}^{o p} | | |
| cardona-qft-methods_FO2412 | 208 | 0.990 | { }^{17,24} | | |
| cardona-qft-methods_FO2413 | 208 | 1.000 | \mathcal{M}_{F} | | |
| cardona-qft-methods_FO2414 | 208 | 0.999 | \mathcal{A}_{L R} | | |
| cardona-qft-methods_FO2415 | 208 | 1.000 | \operatorname{dim}_{\mathbb{C}} \mathcal{M}_{F}=32 | | |
| cardona-qft-methods_FO2416 | 208 | 1.000 | \mathcal{M}_{F}=\mathcal{E} \oplus \mathcal{E}^{0} | | |
| cardona-qft-methods_FO2417 | 208 | 0.993 | \mathbb{C}, \mathbb{H} | | |
| cardona-qft-methods_FO2418 | 208 | 0.993 | M_{3}(\mathbb{C}) | | |
| cardona-qft-methods_FO2419 | 208 | 1.000 | \mathcal{B} | | |
| cardona-qft-methods_FO2420 | 209 | 1.000 | \mathcal{M}_{F} \cong \mathcal{M}_{F}^{0} | | |
| cardona-qft-methods_FO2421 | 209 | 1.000 | J_{F}(\xi, \bar{\eta})= | | |
| cardona-qft-methods_FO2422 | 209 | 1.000 | (\eta, \bar{\xi}) | | |
| cardona-qft-methods_FO2423 | 209 | 1.000 | \xi, \eta \in \mathcal{E} | | |
| cardona-qft-methods_FO2424 | 209 | 1.000 | \mathbb{Z} / 2 \mathbb{Z} | | |
| cardona-qft-methods_FO2425 | 209 | 1.000 | \gamma_{F}=c-J_{F} c J_{F} | | |
| cardona-qft-methods_FO2426 | 209 | 1.000 | c=(0,1,-1,0) \in \mathcal{A}_{L R} | | |
| cardona-qft-methods_FO2427 | 209 | 0.500 | \bmod 8 | | |
| cardona-qft-methods_FO2428 | 209 | 0.899 | |\uparrow\rangle | | |
| cardona-qft-methods_FO2429 | 209 | 0.899 | |\downarrow\rangle | | |
| cardona-qft-methods_FO2430 | 209 | 0.899 | \mathbf{2} | | |
| cardona-qft-methods_FO2431 | 209 | 1.000 | \mathbf{2}_{L} \otimes \mathbf{1}^{0} | | |
| cardona-qft-methods_FO2432 | 209 | 1.000 | \nu_{L} \in|\uparrow\rangle_{L} \otimes \mathbf{1}^{0} | | |
| cardona-qft-methods_FO2433 | 209 | 1.000 | e_{L} \in|\downarrow\rangle_{L} \otimes \mathbf{1}^{0} | | |
| cardona-qft-methods_FO2434 | 209 | 1.000 | \mathbf{2}_{R} \otimes \mathbf{1}^{0} | | |
| cardona-qft-methods_FO2435 | 209 | 1.000 | \nu_{R} \in|\uparrow\rangle_{R} \otimes \mathbf{1}^{0} | | |
| cardona-qft-methods_FO2436 | 209 | 1.000 | e_{R} \in|\downarrow\rangle_{R} \otimes \mathbf{1}^{0} | | |
| cardona-qft-methods_FO2437 | 209 | 0.724 | \mathbf{2}_{L} \otimes \mathbf{3}^{0} | | |
| cardona-qft-methods_FO2438 | 209 | 0.984 | u_{L} \in|\uparrow\rangle_{L} \otimes \mathbf{3}^{0} | | |
| cardona-qft-methods_FO2439 | 209 | 0.984 | d_{L} \in|\downarrow\rangle_{L} \otimes \mathbf{3}^{0} | | |
| cardona-qft-methods_FO2440 | 209 | 0.749 | \mathbf{2}_{R} \otimes \mathbf{3}^{0} | | |
| cardona-qft-methods_FO2441 | 209 | 0.749 | \mathrm{u} / \mathrm{c} / \mathrm{t} | | |
| cardona-qft-methods_FO2442 | 209 | 0.749 | u_{R} \in | | |
| cardona-qft-methods_FO2443 | 209 | 0.967 | |\uparrow\rangle_{R} \otimes \mathbf{3}^{0} | | |
| cardona-qft-methods_FO2444 | 209 | 0.967 | d_{R} \in|\downarrow\rangle_{R} \otimes \mathbf{3}^{0} | | |
| cardona-qft-methods_FO2445 | 209 | 0.999 | \mathbf{1} \otimes \mathbf{2}_{L, R}^{0} | | |
| cardona-qft-methods_FO2446 | 209 | 0.999 | \left.\bar{\nu}_{L, R} \in \mathbf{1} \otimes \uparrow\right\rangle_{L, R}^{0} | | |
| cardona-qft-methods_FO2447 | 209 | 1.000 | \bar{e}_{L, R} \in \mathbf{1} \otimes|\downarrow\rangle_{L, R}^{0} | | |
| cardona-qft-methods_FO2448 | 209 | 1.000 | \mathbf{3} \otimes \mathbf{2}_{L, R}^{0} | | |
| cardona-qft-methods_FO2449 | 209 | 1.000 | \bar{u}_{L, R} \in | | |
| cardona-qft-methods_FO2450 | 209 | 1.000 | \mathbf{3} \otimes|\uparrow\rangle_{L, R}^{0} | | |
| cardona-qft-methods_FO2451 | 209 | 1.000 | \bar{d}_{L, R} \in \mathbf{3} \otimes|\downarrow\rangle_{L, R}^{0} | | |
| cardona-qft-methods_FO2452 | 209 | 1.000 | N=3 | | |
| cardona-qft-methods_FO2453 | 209 | 1.000 | \mathcal{H}_{F}=\mathcal{M}_{F} \oplus \mathcal{M}_{F} \oplus \mathcal{M}_{F} | | |
| cardona-qft-methods_FO2454 | 209 | 1.000 | \left.\left.\pi\right|_{\mathcal{H}_{f}} \oplus \pi^{\prime}\right|_{\mathcal{H}_{\bar{f}}} | | |
| cardona-qft-methods_FO2455 | 209 | 1.000 | \mathcal{H}_{f}=\mathcal{E} \oplus \mathcal{E} \oplus \mathcal{E} | | |
| cardona-qft-methods_FO2456 | 209 | 1.000 | \mathcal{H}_{\bar{f}}=\mathcal{E}^{0} \oplus \mathcal{E}^{0} \oplus \mathcal{E}^{0} | | |
| cardona-qft-methods_FO2457 | 210 | 1.000 | \mathcal{H}_{f} | | |
| cardona-qft-methods_FO2458 | 210 | 1.000 | \mathcal{H}_{\bar{f}} | | |
| cardona-qft-methods_FO2459 | 210 | 1.000 | \left(\mathcal{A}_{F}, D_{F}\right) | | |
| cardona-qft-methods_FO2460 | 210 | 0.973 | \mathcal{A}_{F} \subset \mathcal{A}_{L R} | | |
| cardona-qft-methods_FO2461 | 210 | 0.973 | D_{F} | | |
| cardona-qft-methods_FO2462 | 210 | 0.996 | \mathcal{A}_{F} | | |
| cardona-qft-methods_FO2463 | 210 | 1.000 | \operatorname{Aut}\left(\mathcal{A}_{L R}\right) | | |
| cardona-qft-methods_FO2464 | 210 | 1.000 | \lambda \in \mathrm{U}(1) | | |
| cardona-qft-methods_FO2465 | 210 | 1.000 | \left(\mathcal{A}_{F}, \mathcal{H}_{F}, \gamma_{F}, J_{F}\right) | | |
| cardona-qft-methods_FO2466 | 210 | 1.000 | J_{F} | | |
| cardona-qft-methods_FO2467 | 210 | 1.000 | \gamma_{F} | | |
| cardona-qft-methods_FO2468 | 210 | 1.000 | a, b \in \mathcal{A}_{F} | | |
| cardona-qft-methods_FO2469 | 211 | 1.000 | S_{3} | | |
| cardona-qft-methods_FO2470 | 211 | 1.000 | Y_{(\downarrow 1)}, Y_{(\uparrow 1)}, Y_{(\downarrow 3)}, Y_{(\uparrow 3)} \in \mathrm{GL}_{3}(\mathbb{C}) | | |
| cardona-qft-methods_FO2471 | 211 | 1.000 | Y_{R} | | |
| cardona-qft-methods_FO2472 | 211 | 1.000 | \mathcal{C}_{3} \times \mathcal{C}_{1} | | |
| cardona-qft-methods_FO2473 | 211 | 1.000 | \mathcal{C}_{3} | | |
| cardona-qft-methods_FO2474 | 211 | 1.000 | \left(Y_{(\downarrow 3)}, Y_{(\uparrow 3)}\right) | | |
| cardona-qft-methods_FO2475 | 211 | 1.000 | W_{j} | | |
| cardona-qft-methods_FO2476 | 211 | 1.000 | G=\mathrm{GL}_{3}(\mathbb{C}) | | |
| cardona-qft-methods_FO2477 | 211 | 1.000 | K=U(3) | | |
| cardona-qft-methods_FO2478 | 211 | 1.000 | \operatorname{dim}_{\mathbb{R}} \mathcal{C}_{3}=10= | | |
| cardona-qft-methods_FO2479 | 211 | 0.978 | 3+3+4 | | |
| cardona-qft-methods_FO2480 | 211 | 0.978 | 3+3 | | |
| cardona-qft-methods_FO2481 | 211 | 1.000 | \mathcal{C}_{1} | | |
| cardona-qft-methods_FO2482 | 211 | 1.000 | \left(Y_{(\downarrow 1)}, Y_{(\uparrow 1)}, Y_{R}\right) | | |
| cardona-qft-methods_FO2483 | 211 | 1.000 | \pi: \mathcal{C}_{1} \rightarrow \mathcal{C}_{3} | | |
| cardona-qft-methods_FO2484 | 211 | 1.000 | Y_{R} \mapsto \lambda^{2} Y_{R} | | |
| cardona-qft-methods_FO2485 | 211 | 1.000 | \operatorname{dim}_{\mathbb{R}}\left(\mathcal{C}_{3} \times \mathcal{C}_{1}\right)=31 | | |
| cardona-qft-methods_FO2486 | 211 | 1.000 | 12-1=11 | | |
| cardona-qft-methods_FO2487 | 212 | 1.000 | \delta_{\uparrow}, \delta_{\downarrow} | | |
| cardona-qft-methods_FO2488 | 212 | 1.000 | c_{i}=\cos \theta_{i}, s_{i}=\sin \theta_{i}, e_{\delta}=\exp (i \delta) | | |
| cardona-qft-methods_FO2489 | 212 | 1.000 | U_{C K M} | | |
| cardona-qft-methods_FO2490 | 212 | 1.000 | U_{P M N S} | | |
| cardona-qft-methods_FO2491 | 212 | 0.969 | V^{*} V | | |
| cardona-qft-methods_FO2492 | 212 | 1.000 | (K \times K) \backslash(G \times G) / K | | |
| cardona-qft-methods_FO2493 | 212 | 1.000 | \nu | | |
| cardona-qft-methods_FO2494 | 213 | 0.699 | \left(\mathcal{A}_{i}, \mathcal{H}_{i}, D_{i}, \gamma_{i}, J_{i}\right) | | |
| cardona-qft-methods_FO2495 | 214 | 1.000 | J, \gamma | | |
| cardona-qft-methods_FO2496 | 214 | 1.000 | \zeta_{a, D}(s)= | | |
| cardona-qft-methods_FO2497 | 214 | 1.000 | \operatorname{Tr}\left(a|D|^{-s}\right) | | |
| cardona-qft-methods_FO2498 | 214 | 1.000 | X=M \times F | | |
| cardona-qft-methods_FO2499 | 214 | 0.974 | 10=4+6 | | |
| cardona-qft-methods_FO2500 | 214 | 0.974 | 2 \bmod 8 | | |
| cardona-qft-methods_FO2501 | 214 | 0.983 | \left\{k \in \mathbb{Z}_{\geq 0}, k \leq 4\right\} | | |
| cardona-qft-methods_FO2502 | 214 | 1.000 | \mathcal{E} | | |
| cardona-qft-methods_FO2503 | 214 | 1.000 | \mathcal{E}_{x} | | |
| cardona-qft-methods_FO2504 | 214 | 1.000 | C^{\infty}(M, \mathcal{E}) | | |
| cardona-qft-methods_FO2505 | 214 | 1.000 | \mathcal{D}_{\mathcal{E}}=c \circ\left(\nabla^{\mathcal{E}} \otimes 1+1 \otimes \nabla^{S}\right) | | |
| cardona-qft-methods_FO2506 | 215 | 0.998 | \mathrm{U}(\mathcal{A})=\left\{u \in \mathcal{A} \mid u u^{*}=\right. | | |
| cardona-qft-methods_FO2507 | 215 | 0.999 | \left.u^{*} u=1\right\} | | |
| cardona-qft-methods_FO2508 | 216 | 1.000 | \operatorname{Ad}(u) | | |
| cardona-qft-methods_FO2509 | 216 | 0.991 | U(1), S U(2) | | |
| cardona-qft-methods_FO2510 | 216 | 1.000 | A^{(1,0)}=\sum_{i} a_{i}\left[\not \partial_{M} \otimes\right. | | |
| cardona-qft-methods_FO2511 | 216 | 0.749 | \left.1, a_{i}^{\prime}\right] | | |
| cardona-qft-methods_FO2512 | 216 | 0.749 | a_{i}=\left(\lambda_{i}, q_{i}, m_{i}\right) | | |
| cardona-qft-methods_FO2513 | 216 | 0.749 | a_{i}^{\prime}=\left(\lambda_{i}^{\prime}, q_{i}^{\prime}, m_{i}^{\prime}\right) | | |
| cardona-qft-methods_FO2514 | 216 | 0.749 | \mathcal{A}=C^{\infty}\left(M, \mathcal{A}_{F}\right) | | |
| cardona-qft-methods_FO2515 | 216 | 1.000 | \Lambda=\sum_{i} \lambda_{i} d \lambda_{i}^{\prime}=\sum_{i} \lambda_{i}\left[\not \partial_{M} \otimes 1, \lambda_{i}^{\prime}\right] | | |
| cardona-qft-methods_FO2516 | 216 | 0.988 | Q=\sum_{i} q_{i} d q_{i}^{\prime} | | |
| cardona-qft-methods_FO2517 | 216 | 0.988 | q=f_{0}+\sum_{\alpha} i f_{\alpha} \sigma^{\alpha} | | |
| cardona-qft-methods_FO2518 | 216 | 0.988 | Q= | | |
| cardona-qft-methods_FO2519 | 216 | 0.966 | \sum_{\alpha} f_{\alpha}\left[\not \partial_{M} \otimes 1, i f_{\alpha}^{\prime} \sigma^{\alpha}\right] ; | | |
| cardona-qft-methods_FO2520 | 216 | 1.000 | U(3) | | |
| cardona-qft-methods_FO2521 | 216 | 1.000 | V^{\prime}=\sum_{i} m_{i} d m_{i}^{\prime}=\sum_{i} m_{i}\left[\not \partial_{M} \otimes 1, m_{i}^{\prime}\right] | | |
| cardona-qft-methods_FO2522 | 216 | 0.806 | V^{\prime} | | |
| cardona-qft-methods_FO2523 | 216 | 1.000 | \operatorname{SU}\left(\mathcal{A}_{F}\right) | | |
| cardona-qft-methods_FO2524 | 216 | 1.000 | \operatorname{Tr}(A)=0 | | |
| cardona-qft-methods_FO2525 | 216 | 1.000 | (1,0) | | |
| cardona-qft-methods_FO2526 | 216 | 1.000 | A+J A J^{-1} | | |
| cardona-qft-methods_FO2527 | 217 | 1.000 | A^{(0,1)} | | |
| cardona-qft-methods_FO2528 | 217 | 1.000 | \varphi_{1}=\sum \lambda_{i}\left(\alpha_{i}^{\prime}-\lambda_{i}^{\prime}\right), \varphi_{2}=\sum \lambda_{i} \beta_{i}^{\prime} \varphi_{1}^{\prime}=\sum \alpha_{i}\left(\lambda_{i}^{\prime}-\alpha_{i}^{\prime}\right)+\beta_{i} \bar{\beta}_{i}^{\prime} | | |
| cardona-qft-methods_FO2529 | 217 | 1.000 | \varphi_{2}^{\prime}=\sum\left(-\alpha_{i} \beta_{i}^{\prime}+\beta_{i}\left(\bar{\lambda}_{i}^{\prime}-\bar{\alpha}_{i}^{\prime}\right)\right) | | |
| cardona-qft-methods_FO2530 | 217 | 1.000 | a_{i}(x)=\left(\lambda_{i}, q_{i}, m_{i}\right) | | |
| cardona-qft-methods_FO2531 | 217 | 1.000 | a_{i}^{\prime}(x)=\left(\lambda_{i}^{\prime}, q_{i}^{\prime}, m_{i}^{\prime}\right) | | |
| cardona-qft-methods_FO2532 | 217 | 1.000 | H=\varphi_{1}+\varphi_{2} j | | |
| cardona-qft-methods_FO2533 | 217 | 1.000 | \varphi=\left(\varphi_{1}, \varphi_{2}\right) | | |
| cardona-qft-methods_FO2534 | 217 | 0.998 | D_{A}^{2}=\nabla^{*} \nabla-E | | |
| cardona-qft-methods_FO2535 | 217 | 0.998 | \nabla^{*} \nabla | | |
| cardona-qft-methods_FO2536 | 217 | 0.998 | \nabla=\nabla^{s}+\mathbb{A} | | |
| cardona-qft-methods_FO2537 | 218 | 0.996 | s=-R | | |
| cardona-qft-methods_FO2538 | 218 | 0.996 | \mathbb{F}_{\mu \nu} | | |
| cardona-qft-methods_FO2539 | 218 | 0.996 | \mathbb{A} | | |
| cardona-qft-methods_FO2540 | 218 | 1.000 | D / \Lambda | | |
| cardona-qft-methods_FO2541 | 218 | 1.000 | f>0 | | |
| cardona-qft-methods_FO2542 | 218 | 1.000 | f_{k}=\int_{0}^{\infty} f(v) v^{k-1} d v | | |
| cardona-qft-methods_FO2543 | 218 | 0.999 | \operatorname{DimSp}(\mathcal{A}, \mathcal{H}, D) | | |
| cardona-qft-methods_FO2544 | 218 | 1.000 | \zeta_{b, D}(s)=\operatorname{Tr}\left(b|D|^{-s}\right) | | |
| cardona-qft-methods_FO2545 | 218 | 1.000 | a_{\alpha} | | |
| cardona-qft-methods_FO2546 | 218 | 1.000 | \alpha<0 | | |
| cardona-qft-methods_FO2547 | 218 | 1.000 | \zeta_{D} | | |
| cardona-qft-methods_FO2548 | 219 | 1.000 | \int_{0}^{1} t^{\alpha+s / 2-1} d t=(\alpha+s / 2)^{-1} | | |
| cardona-qft-methods_FO2549 | 219 | 1.000 | \zeta_{D}(0)=a_{0} | | |
| cardona-qft-methods_FO2550 | 219 | 1.000 | a_{0} \int_{0}^{1} t^{s / 2-1} d t=a_{0} \frac{2}{s} | | |
| cardona-qft-methods_FO2551 | 219 | 1.000 | \mathcal{H}_{c l}^{+} | | |
| cardona-qft-methods_FO2552 | 219 | 0.999 | \mathfrak{A}(\tilde{\xi}) | | |
| cardona-qft-methods_FO2553 | 219 | 1.000 | \left\langle\xi, D_{A} \xi\right\rangle | | |
| cardona-qft-methods_FO2554 | 220 | 1.000 | f_{0}, f_{2}, f_{4} | | |
| cardona-qft-methods_FO2555 | 220 | 1.000 | f_{0}=f(0) | | |
| cardona-qft-methods_FO2556 | 220 | 1.000 | k>0 | | |
| cardona-qft-methods_FO2557 | 220 | 0.997 | \mathfrak{a}, \mathfrak{b}, \mathfrak{c}, \mathfrak{d}, \mathfrak{e} | | |
| cardona-qft-methods_FO2558 | 221 | 1.000 | P=-\left(g^{\mu \nu} I \partial_{\mu} \partial_{\nu}+A^{\mu} \partial_{\mu}+B\right) | | |
| cardona-qft-methods_FO2559 | 221 | 1.000 | m=\operatorname{dim} M | | |
| cardona-qft-methods_FO2560 | 221 | 1.000 | P=\nabla^{*} \nabla-E | | |
| cardona-qft-methods_FO2561 | 221 | 1.000 | E_{; \mu}{ }^{\mu}:=\nabla_{\mu} \nabla^{\mu} E | | |
| cardona-qft-methods_FO2562 | 221 | 0.712 | H=\frac{\sqrt{\mathfrak{a} f_{0}}}{\pi} \varphi | | |
| cardona-qft-methods_FO2563 | 222 | 1.000 | R^{*} R^{*}=\frac{1}{4} \epsilon^{\mu \nu \rho \sigma} \epsilon_{\alpha \beta \gamma \delta} R_{\mu \nu}^{\alpha \beta} R_{\rho \sigma}^{\gamma \delta} | | |
| cardona-qft-methods_FO2564 | 222 | 1.000 | \chi(M) | | |
| cardona-qft-methods_FO2565 | 222 | 1.000 | C^{\mu \nu \rho \sigma} | | |
| cardona-qft-methods_FO2566 | 222 | 1.000 | 10^{15} | | |
| cardona-qft-methods_FO2567 | 222 | 1.000 | 10^{17} \mathrm{GeV} | | |
| cardona-qft-methods_FO2568 | 222 | 1.000 | f_{0} | | |
| cardona-qft-methods_FO2569 | 223 | 1.000 | { }^{17,29,30,33} | | |
| cardona-qft-methods_FO2570 | 234 | 1.000 | \nu M S M | | |
| cardona-qft-methods_FO2571 | 223 | 0.999 | \Lambda \frac{d f}{d \Lambda}=\beta_{f}(\Lambda) | | |
| cardona-qft-methods_FO2572 | 224 | 0.978 | \Lambda_{\text {unif }} | | |
| cardona-qft-methods_FO2573 | 224 | 0.822 | Y_{\nu}^{(3)} | | |
| cardona-qft-methods_FO2574 | 224 | 1.000 | Y_{\nu} | | |
| cardona-qft-methods_FO2575 | 224 | 1.000 | M^{(3)} | | |
| cardona-qft-methods_FO2576 | 224 | 0.997 | Y_{\nu}^{(2)} | | |
| cardona-qft-methods_FO2577 | 224 | 0.997 | M^{(2)} | | |
| cardona-qft-methods_FO2578 | 224 | 1.000 | Y_{\nu}^{(1)} | | |
| cardona-qft-methods_FO2579 | 224 | 1.000 | M^{(1)} | | |
| cardona-qft-methods_FO2580 | 224 | 1.000 | \Lambda_{e w} | | |
| cardona-qft-methods_FO2581 | 224 | 1.000 | Y_{\nu}^{(N)} | | |
| cardona-qft-methods_FO2582 | 224 | 1.000 | M^{(N)} | | |
| cardona-qft-methods_FO2583 | 225 | 1.000 | t=\log \left(\Lambda / M_{Z}\right) | | |
| cardona-qft-methods_FO2584 | 225 | 1.000 | \Lambda=M_{Z} | | |
| cardona-qft-methods_FO2585 | 225 | 1.000 | g_{3}^{2}=g_{2}^{2}=5 g_{1}^{2} / 3 | | |
| cardona-qft-methods_FO2586 | 226 | 0.994 | \mathfrak{c} | | |
| cardona-qft-methods_FO2587 | 227 | 1.000 | g_{1}, g_{2}, g_{3} | | |
| cardona-qft-methods_FO2588 | 228 | 1.000 | \tilde{\lambda} | | |
| cardona-qft-methods_FO2589 | 228 | 1.000 | |\mathbf{H}|^{4} | | |
| cardona-qft-methods_FO2590 | 228 | 0.585 | \lambda\left(M_{Z}\right) \sim 0.241 | | |
| cardona-qft-methods_FO2591 | 228 | 0.585 | \sim 170 \mathrm{GeV} | | |
| cardona-qft-methods_FO2592 | 229 | 1.000 | \kappa_{0}, \gamma_{0}, \alpha_{0}, \tau_{0}, \mu_{0}, \xi_{0}, \lambda_{0} | | |
| cardona-qft-methods_FO2593 | 229 | 0.609 | { }^{3,18,27} | | |
| cardona-qft-methods_FO2594 | 230 | 1.000 | 10^{-12} | | |
| cardona-qft-methods_FO2595 | 230 | 1.000 | \lambda_{0}=\lambda \cdot\left(\pi^{2} \mathfrak{b}\right) /\left(f_{0} \mathfrak{a}^{2}\right) | | |
| cardona-qft-methods_FO2596 | 230 | 0.992 | x_{j} | | |
| cardona-qft-methods_FO2597 | 230 | 0.992 | \beta_{j}^{\mathrm{SM}} | | |
| cardona-qft-methods_FO2598 | 230 | 1.000 | \beta_{j}^{\text {grav }} | | |
| cardona-qft-methods_FO2599 | 230 | 1.000 | \rho_{0} \sim 0.024 | | |
| cardona-qft-methods_FO2600 | 230 | 1.000 | a_{1}= | | |
| cardona-qft-methods_FO2601 | 230 | 0.993 | a_{2}=a_{3}=a_{g} | | |
| cardona-qft-methods_FO2602 | 230 | 0.993 | \left|a_{g}\right| \sim 1 | | |
| cardona-qft-methods_FO2603 | 230 | 0.473 | a_{g} \leq a_{y}<0 | | |
| cardona-qft-methods_FO2604 | 230 | 0.473 | a_{\lambda} | | |
| cardona-qft-methods_FO2605 | 230 | 0.473 | \left(\right. | | |
| cardona-qft-methods_FO2606 | 230 | 0.473 | \left.^{45}\right) | | |
| cardona-qft-methods_FO2607 | 231 | 1.000 | m_{H} \sim 125.4 | | |
| cardona-qft-methods_FO2608 | 231 | 0.999 | m_{t} \sim 171.3 \mathrm{GeV} | | |
| cardona-qft-methods_FO2609 | 231 | 1.000 | { }^{42-44} | | |
| cardona-qft-methods_FO2610 | 236 | 1.000 | 10^{-32} | | |
| cardona-qft-methods_FO2611 | 236 | 1.000 | 10^{9} | | |
| cardona-qft-methods_FO2612 | 236 | 1.000 | L \simeq 10^{-32} \mathrm{~cm} | | |
| cardona-qft-methods_FO2613 | 236 | 1.000 | \lambda_{C} | | |
| cardona-qft-methods_FO2614 | 236 | 1.000 | L^{3} \simeq\left(10^{-32} \mathrm{~cm}\right)^{3} | | |
| cardona-qft-methods_FO2615 | 236 | 1.000 | \Delta x | | |
| cardona-qft-methods_FO2616 | 236 | 1.000 | \Delta p | | |
| cardona-qft-methods_FO2617 | 236 | 0.994 | x p-p x=i \hbar | | |
| cardona-qft-methods_FO2618 | 236 | 1.000 | \Delta y | | |
| cardona-qft-methods_FO2619 | 237 | 0.640 | G-M | | |
| cardona-qft-methods_FO2620 | 237 | 0.640 | \mathcal{A}_{\theta} | | |
| cardona-qft-methods_FO2621 | 237 | 0.640 | \mathbb{R}^{d+1} | | |
| cardona-qft-methods_FO2622 | 238 | 1.000 | \mathbb{C} G | | |
| cardona-qft-methods_FO2623 | 238 | 1.000 | U(g) \Psi | | |
| cardona-qft-methods_FO2624 | 239 | 1.000 | \mathcal{H}^{(1)} | | |
| cardona-qft-methods_FO2625 | 239 | 1.000 | |0\rangle | | |
| cardona-qft-methods_FO2626 | 239 | 1.000 | \mathcal{H}^{(N)}=\mathcal{H}^{(1)} \otimes \cdots \otimes \mathcal{H}^{(1)} | | |
| cardona-qft-methods_FO2627 | 239 | 1.000 | \mathcal{F}=\bigoplus_{N} \mathcal{H}^{(N)} | | |
| cardona-qft-methods_FO2628 | 239 | 1.000 | U^{(N)} | | |
| cardona-qft-methods_FO2629 | 239 | 1.000 | \mathcal{H}^{(N)} | | |
| cardona-qft-methods_FO2630 | 239 | 1.000 | U^{(1)} | | |
| cardona-qft-methods_FO2631 | 240 | 1.000 | \alpha^{*} | | |
| cardona-qft-methods_FO2632 | 240 | 1.000 | \beta^{*} | | |
| cardona-qft-methods_FO2633 | 240 | 1.000 | \alpha * \beta | | |
| cardona-qft-methods_FO2634 | 240 | 1.000 | { }^{7,8} | | |
| cardona-qft-methods_FO2635 | 240 | 1.000 | \mathcal{F} | | |
| cardona-qft-methods_FO2636 | 240 | 1.000 | U^{(N)}(N \geq 2) | | |
| cardona-qft-methods_FO2637 | 240 | 1.000 | \mathbb{C} G \otimes \mathbb{C} G | | |
| cardona-qft-methods_FO2638 | 240 | 1.000 | U^{(0)} | | |
| cardona-qft-methods_FO2639 | 240 | 1.000 | U^{(0)}(g)|0\rangle=|0\rangle | | |
| cardona-qft-methods_FO2640 | 241 | 1.000 | D(g) | | |
| cardona-qft-methods_FO2641 | 241 | 1.000 | U^{(1)}(g) | | |
| cardona-qft-methods_FO2642 | 241 | 1.000 | U^{(2)} | | |
| cardona-qft-methods_FO2643 | 241 | 1.000 | \Delta: G \rightarrow \mathbb{C} G \otimes \mathbb{C} G | | |
| cardona-qft-methods_FO2644 | 241 | 1.000 | U^{(2)}(g)=U^{(1)} \otimes U^{(1)} \Delta(g) | | |
| cardona-qft-methods_FO2645 | 241 | 1.000 | \Delta: \mathbb{C} G \rightarrow \mathbb{C} G \otimes \mathbb{C} G | | |
| cardona-qft-methods_FO2646 | 241 | 1.000 | \Delta(g)=g \otimes g | | |
| cardona-qft-methods_FO2647 | 242 | 1.000 | \mathcal{E}_{3} | | |
| cardona-qft-methods_FO2648 | 242 | 1.000 | g \in \mathcal{E}_{3} | | |
| cardona-qft-methods_FO2649 | 242 | 1.000 | \theta_{\mu \nu} | | |
| cardona-qft-methods_FO2650 | 242 | 1.000 | P_{\nu} | | |
| cardona-qft-methods_FO2651 | 242 | 1.000 | G \otimes G | | |
| cardona-qft-methods_FO2652 | 242 | 1.000 | \mathcal{P}_{+}^{\uparrow} | | |
| cardona-qft-methods_FO2653 | 242 | 1.000 | \Delta_{\theta} | | |
| cardona-qft-methods_FO2654 | 243 | 1.000 | g^{-1} | | |
| cardona-qft-methods_FO2655 | 243 | 1.000 | g \rightarrow g^{-1} | | |
| cardona-qft-methods_FO2656 | 243 | 1.000 | (S(g h)=S(h) S(g)) | | |
| cardona-qft-methods_FO2657 | 243 | 0.954 | U\left(g^{-1}\right)=U(g)^{*} | | |
| cardona-qft-methods_FO2658 | 243 | 0.970 | U\left(\hat{\alpha}^{*}\right)=U(\hat{\alpha})^{*} . U | | |
| cardona-qft-methods_FO2659 | 243 | 1.000 | (\alpha \beta) \gamma=\alpha(\beta \gamma) | | |
| cardona-qft-methods_FO2660 | 243 | 1.000 | \alpha, \beta, \gamma \in H | | |
| cardona-qft-methods_FO2661 | 244 | 1.000 | *: \alpha \in H \rightarrow \alpha^{*} \in H | | |
| cardona-qft-methods_FO2662 | 244 | 0.953 | (\alpha \beta)^{*}=\beta^{*} \alpha^{*}, \alpha, \beta \in H | | |
| cardona-qft-methods_FO2663 | 244 | 0.992 | (\lambda \alpha)^{*}=\bar{\lambda} \alpha^{*} \quad \lambda \in \mathbb{C}, \alpha \in H | | |
| cardona-qft-methods_FO2664 | 244 | 0.719 | e^{*}=e, \quad \alpha e=e \alpha=\alpha, \forall \alpha \in H | | |
| cardona-qft-methods_FO2665 | 244 | 0.672 | \epsilon: H \rightarrow \mathbb{C} | | |
| cardona-qft-methods_FO2666 | 244 | 0.683 | S: H \rightarrow H | | |
| cardona-qft-methods_FO2667 | 244 | 0.683 | S(\alpha \beta)=S(\beta \alpha) | | |
| cardona-qft-methods_FO2668 | 244 | 1.000 | m_{13} \otimes m_{24} | | |
| cardona-qft-methods_FO2669 | 244 | 1.000 | H \otimes H \otimes H \otimes H | | |
| cardona-qft-methods_FO2670 | 245 | 1.000 | b | | |
| cardona-qft-methods_FO2671 | 245 | 1.000 | b^{n}=0 | | |
| cardona-qft-methods_FO2672 | 245 | 1.000 | a b=r b a | | |
| cardona-qft-methods_FO2673 | 245 | 0.999 | \Delta(a)=a \otimes a, \Delta(b)=a \otimes b+b \otimes a^{-1}, \epsilon(a)=1, \epsilon(b)=0 | | |
| cardona-qft-methods_FO2674 | 245 | 0.998 | H \otimes H | | |
| cardona-qft-methods_FO2675 | 245 | 1.000 | \Delta_{F} | | |
| cardona-qft-methods_FO2676 | 245 | 1.000 | \Delta_{F}(h)=F^{-1} \Delta(h) F | | |
| cardona-qft-methods_FO2677 | 245 | 1.000 | \left(\Delta_{F} \otimes I d\right) \Delta_{F}=\left(I d \otimes \Delta_{F}\right) \Delta_{F} | | |
| cardona-qft-methods_FO2678 | 245 | 1.000 | U_{q}(S L(S, \mathbb{C})) | | |
| cardona-qft-methods_FO2679 | 245 | 1.000 | { }^{6,7,9-12} | | |
| cardona-qft-methods_FO2680 | 245 | 1.000 | V \otimes V | | |
| cardona-qft-methods_FO2681 | 245 | 1.000 | \xi \otimes \eta \in V \otimes V | | |
| cardona-qft-methods_FO2682 | 245 | 0.744 | (\rho \otimes \rho) \Delta(g) | | |
| cardona-qft-methods_FO2683 | 245 | 1.000 | V \otimes_{S} V | | |
| cardona-qft-methods_FO2684 | 246 | 0.985 | V \otimes_{A} V | | |
| cardona-qft-methods_FO2685 | 246 | 1.000 | V \otimes V \otimes \cdots \otimes V | | |
| cardona-qft-methods_FO2686 | 246 | 1.000 | S_{N} | | |
| cardona-qft-methods_FO2687 | 246 | 1.000 | \tau_{i, i+1} \rightarrow \pm 1 | | |
| cardona-qft-methods_FO2688 | 246 | 1.000 | V \otimes_{S, A} V \otimes_{S, A} \cdots \otimes_{S, A} V \equiv V^{\otimes_{S}}, V^{\otimes_{A}} | | |
| cardona-qft-methods_FO2689 | 246 | 0.998 | \Delta^{\mathrm{op}} | | |
| cardona-qft-methods_FO2690 | 246 | 1.000 | R \in H \otimes H | | |
| cardona-qft-methods_FO2691 | 246 | 1.000 | \Delta^{\mathrm{op}}(\eta)= | | |
| cardona-qft-methods_FO2692 | 246 | 1.000 | R \Delta(\eta) R^{-1} | | |
| cardona-qft-methods_FO2693 | 246 | 0.658 | r h o | | |
| cardona-qft-methods_FO2694 | 246 | 1.000 | (\rho \otimes \rho) \Delta(\alpha) | | |
| cardona-qft-methods_FO2695 | 246 | 1.000 | \tau(\rho \otimes \rho) R | | |
| cardona-qft-methods_FO2696 | 246 | 1.000 | \tau R | | |
| cardona-qft-methods_FO2697 | 247 | 1.000 | \tau_{i, i+1} | | |
| cardona-qft-methods_FO2698 | 247 | 1.000 | \mathcal{B}_{N} | | |
| cardona-qft-methods_FO2699 | 247 | 1.000 | R \Delta R^{-1} | | |
| cardona-qft-methods_FO2700 | 247 | 0.974 | \Delta_{\mathrm{op}} | | |
| cardona-qft-methods_FO2701 | 247 | 1.000 | (\rho \otimes \rho) \Delta_{0}(g) | | |
| cardona-qft-methods_FO2702 | 247 | 1.000 | \Delta_{\theta}(g) | | |
| cardona-qft-methods_FO2703 | 247 | 1.000 | (\rho \otimes \rho) \Delta_{\theta}(g) | | |
| cardona-qft-methods_FO2704 | 247 | 1.000 | \tau_{\theta} | | |
| cardona-qft-methods_FO2705 | 247 | 0.666 | \Delta_{\theta}^{\mathrm{op}} | | |
| cardona-qft-methods_FO2706 | 247 | 1.000 | \Delta_{\theta}^{\mathrm{op}}(g)=F_{\theta}(g \otimes g) F_{\theta}^{-1} | | |
| cardona-qft-methods_FO2707 | 247 | 1.000 | R_{\theta} \Delta_{\theta}(g)=\Delta_{\theta}^{\mathrm{op}}(g) R_{\theta} | | |
| cardona-qft-methods_FO2708 | 247 | 1.000 | \tau_{\theta}^{2}=\mathrm{Id} | | |
| cardona-qft-methods_FO2709 | 248 | 1.000 | R(t) | | |
| cardona-qft-methods_FO2710 | 248 | 1.000 | t<0 | | |
| cardona-qft-methods_FO2711 | 248 | 1.000 | A>B | | |
| cardona-qft-methods_FO2712 | 248 | 1.000 | O | | |
| cardona-qft-methods_FO2713 | 248 | 1.000 | C>O | | |
| cardona-qft-methods_FO2714 | 248 | 1.000 | O>A | | |
| cardona-qft-methods_FO2715 | 248 | 0.817 | > | | |
| cardona-qft-methods_FO2716 | 248 | 1.000 | \rho(x), \eta(y) | | |
| cardona-qft-methods_FO2717 | 249 | 1.000 | x_{\mu} | | |
| cardona-qft-methods_FO2718 | 249 | 1.000 | \widehat{x}_{\mu} | | |
| cardona-qft-methods_FO2719 | 249 | 1.000 | G M | | |
| cardona-qft-methods_FO2720 | 249 | 1.000 | \mathcal{H}_{i} | | |
| cardona-qft-methods_FO2721 | 249 | 1.000 | g \rightarrow U_{i}(g) | | |
| cardona-qft-methods_FO2722 | 249 | 1.000 | \mathcal{H}_{1} \otimes \mathcal{H}_{2} | | |
| cardona-qft-methods_FO2723 | 250 | 1.000 | m_{0} | | |
| cardona-qft-methods_FO2724 | 250 | 1.000 | \mathcal{A}_{0} | | |
| cardona-qft-methods_FO2725 | 250 | 1.000 | x \in \mathbb{R}^{N} | | |
| cardona-qft-methods_FO2726 | 250 | 1.000 | \mathcal{A}_{\theta}\left(\mathbb{R}^{N}\right) | | |
| cardona-qft-methods_FO2727 | 250 | 1.000 | m_{\theta} | | |
| cardona-qft-methods_FO2728 | 250 | 1.000 | \theta^{\mu \nu}=0 | | |
| cardona-qft-methods_FO2729 | 250 | 1.000 | \mathcal{A}_{0} \otimes \mathcal{A}_{0} | | |
| cardona-qft-methods_FO2730 | 250 | 1.000 | \Delta_{0} | | |
| cardona-qft-methods_FO2731 | 250 | 1.000 | \mathcal{A}_{\theta} \otimes \mathcal{A}_{\theta} | | |
| cardona-qft-methods_FO2732 | 250 | 1.000 | \theta_{\mu \nu}=0 | | |
| cardona-qft-methods_FO2733 | 251 | 1.000 | \tau_{0} | | |
| cardona-qft-methods_FO2734 | 251 | 1.000 | \Delta_{0}(\Lambda)=\Lambda \otimes \Lambda | | |
| cardona-qft-methods_FO2735 | 251 | 1.000 | \phi \otimes \chi | | |
| cardona-qft-methods_FO2736 | 252 | 1.000 | \mathcal{P} | | |
| cardona-qft-methods_FO2737 | 252 | 1.000 | M^{d+1} | | |
| cardona-qft-methods_FO2738 | 252 | 1.000 | \mathcal{A}_{0}\left(M^{d+1}\right) | | |
| cardona-qft-methods_FO2739 | 252 | 1.000 | \varphi | | |
| cardona-qft-methods_FO2740 | 252 | 1.000 | \varphi \in L(\mathcal{H}) \otimes S\left(M^{d+1}\right) | | |
| cardona-qft-methods_FO2741 | 252 | 1.000 | L(\mathcal{H}) | | |
| cardona-qft-methods_FO2742 | 252 | 1.000 | S\left(M^{d+1}\right) | | |
| cardona-qft-methods_FO2743 | 253 | 1.000 | \varphi \otimes \varphi \otimes \ldots \otimes \varphi | | |
| cardona-qft-methods_FO2744 | 253 | 1.000 | L(\mathcal{H}) \otimes\left(S\left(M^{d+1}\right) \otimes S\left(M^{d+1}\right) \otimes \ldots \otimes S\left(M^{d+1}\right)\right. | | |
| cardona-qft-methods_FO2745 | 253 | 1.000 | x_{1}, x_{2}, \ldots x_{N} | | |
| cardona-qft-methods_FO2746 | 253 | 1.000 | \varphi^{\otimes N}=\varphi \otimes \varphi \otimes \ldots \otimes \varphi \in L(\mathcal{H}) \otimes\left(S\left(M^{d+1}\right)^{\otimes N}\right. | | |
| cardona-qft-methods_FO2747 | 253 | 1.000 | U(a, \Lambda) | | |
| cardona-qft-methods_FO2748 | 253 | 1.000 | S\left(M^{d+1}\right)^{\otimes N} | | |
| cardona-qft-methods_FO2749 | 253 | 1.000 | (a, \Lambda) | | |
| cardona-qft-methods_FO2750 | 253 | 1.000 | \Delta_{0}^{N} | | |
| cardona-qft-methods_FO2751 | 253 | 1.000 | (a, \Lambda) \in \mathcal{P} | | |
| cardona-qft-methods_FO2752 | 253 | 1.000 | c_{p}, c_{p}^{\dagger} | | |
| cardona-qft-methods_FO2753 | 253 | 1.000 | \varphi^{( \pm)} | | |
| cardona-qft-methods_FO2754 | 253 | 1.000 | \varphi^{(-)} | | |
| cardona-qft-methods_FO2755 | 253 | 1.000 | P_{\mu} | | |
| cardona-qft-methods_FO2756 | 254 | 0.999 | \mathcal{P}_{\mu}=-i \partial_{\mu} | | |
| cardona-qft-methods_FO2757 | 254 | 1.000 | \mathcal{P}_{\mu} | | |
| cardona-qft-methods_FO2758 | 254 | 0.999 | \underline{\nu} | | |
| cardona-qft-methods_FO2759 | 254 | 0.999 | \widehat{P}_{\mu} | | |
| cardona-qft-methods_FO2760 | 254 | 1.000 | \underline{\nu}\left(\widehat{P}_{\mu}\right)=\mathcal{P}_{\mu} | | |
| cardona-qft-methods_FO2761 | 254 | 1.000 | e_{p} | | |
| cardona-qft-methods_FO2762 | 254 | 1.000 | \Lambda e_{p}=e_{\Lambda p} | | |
| cardona-qft-methods_FO2763 | 254 | 1.000 | d \geq 3 | | |
| cardona-qft-methods_FO2764 | 255 | 0.964 | (a, \Delta) | | |
| cardona-qft-methods_FO2765 | 255 | 0.964 | e_{p_{1}} \otimes e_{p_{2}} \otimes \ldots \otimes e_{p_{N}} | | |
| cardona-qft-methods_FO2766 | 255 | 1.000 | e_{p_{i}} | | |
| cardona-qft-methods_FO2767 | 255 | 1.000 | \mathbb{C} \mathcal{P} | | |
| cardona-qft-methods_FO2768 | 255 | 1.000 | \mathbb{C} S_{N} | | |
| cardona-qft-methods_FO2769 | 255 | 0.833 | U(k) | | |
| cardona-qft-methods_FO2770 | 255 | 1.000 | \mathbb{C}^{k} | | |
| cardona-qft-methods_FO2771 | 255 | 1.000 | \mathbb{C}^{k \otimes N} | | |
| cardona-qft-methods_FO2772 | 255 | 1.000 | \mathbb{C} U(k) | | |
| cardona-qft-methods_FO2773 | 255 | 1.000 | \tau_{i j} | | |
| cardona-qft-methods_FO2774 | 255 | 0.999 | \alpha: p \rightarrow \alpha p, p \in M | | |
| cardona-qft-methods_FO2775 | 256 | 1.000 | \mathbb{C}^{\infty}(M) | | |
| cardona-qft-methods_FO2776 | 256 | 1.000 | f_{1}, f_{2} \in C^{\infty}(M) | | |
| cardona-qft-methods_FO2777 | 256 | 1.000 | C^{0}(M) | | |
| cardona-qft-methods_FO2778 | 256 | 1.000 | C^{\star} | | |
| cardona-qft-methods_FO2779 | 256 | 1.000 | \Psi^{\dagger} | | |
| cardona-qft-methods_FO2780 | 256 | 0.996 | U(a, \Delta) | | |
| cardona-qft-methods_FO2781 | 256 | 1.000 | \mathcal{A}_{\theta}\left(M^{d+1}\right) | | |
| cardona-qft-methods_FO2782 | 256 | 1.000 | M^{(d+1)} | | |
| cardona-qft-methods_FO2783 | 257 | 0.978 | \mathcal{A}_{\theta}\left(M^{(d+1)}\right. | | |
| cardona-qft-methods_FO2784 | 257 | 1.000 | F_{\theta} | | |
| cardona-qft-methods_FO2785 | 257 | 1.000 | \hat{P}_{\mu} | | |
| cardona-qft-methods_FO2786 | 257 | 1.000 | \varphi_{\theta} | | |
| cardona-qft-methods_FO2787 | 257 | 1.000 | U_{\theta} | | |
| cardona-qft-methods_FO2788 | 257 | 1.000 | \varphi_{\theta}^{\dagger} | | |
| cardona-qft-methods_FO2789 | 257 | 1.000 | U_{\theta}(a, \Lambda)|0\rangle=|0\rangle | | |
| cardona-qft-methods_FO2790 | 258 | 1.000 | a_{p}, a_{p}^{\dagger} | | |
| cardona-qft-methods_FO2791 | 258 | 1.000 | e_{p_{1}} \otimes e_{p_{2}} | | |
| cardona-qft-methods_FO2792 | 258 | 1.000 | a_{p_{1}}^{\dagger} | | |
| cardona-qft-methods_FO2793 | 258 | 1.000 | P_{\mu}^{\theta} | | |
| cardona-qft-methods_FO2794 | 258 | 1.000 | a_{p}^{\dagger} | | |
| cardona-qft-methods_FO2795 | 258 | 1.000 | c_{p}^{\dagger} | | |
| cardona-qft-methods_FO2796 | 258 | 0.996 | c_{p} | | |
| cardona-qft-methods_FO2797 | 258 | 0.996 | \varphi_{0} \equiv \varphi: | | |
| cardona-qft-methods_FO2798 | 258 | 1.000 | \varphi_{0} \rightarrow \varphi_{\theta} | | |
| cardona-qft-methods_FO2799 | 258 | 1.000 | \varphi_{0} | | |
| cardona-qft-methods_FO2800 | 259 | 0.999 | \langle 0| | | |
| cardona-qft-methods_FO2801 | 259 | 1.000 | \alpha, \beta | | |
| cardona-qft-methods_FO2802 | 259 | 1.000 | S_{2} | | |
| cardona-qft-methods_FO2803 | 259 | 1.000 | S_{\theta} | | |
| cardona-qft-methods_FO2804 | 260 | 0.932 | a^{\dagger} | | |
| cardona-qft-methods_FO2805 | 260 | 0.932 | \mathcal{F}_{\theta}^{i j} | | |
| cardona-qft-methods_FO2806 | 260 | 0.939 | \partial_{\mu} \otimes \partial_{\nu}, \partial_{\mu} | | |
| cardona-qft-methods_FO2807 | 260 | 0.939 | i^{\text {th }} | | |
| cardona-qft-methods_FO2808 | 260 | 0.939 | \partial_{\nu} | | |
| cardona-qft-methods_FO2809 | 260 | 0.939 | j^{\text {th }} | | |
| cardona-qft-methods_FO2810 | 260 | 0.976 | \tau_{0}^{i j} | | |
| cardona-qft-methods_FO2811 | 260 | 0.976 | i^{t h} | | |
| cardona-qft-methods_FO2812 | 260 | 0.999 | \tau_{\theta}^{i, i+1} \mathrm{~s} | | |
| cardona-qft-methods_FO2813 | 260 | 1.000 | \varphi_{0}^{*}=\varphi_{0} | | |
| cardona-qft-methods_FO2814 | 260 | 1.000 | \varphi_{\theta}^{*}=\varphi_{\theta} | | |
| cardona-qft-methods_FO2815 | 260 | 1.000 | \partial_{\mu} | | |
| cardona-qft-methods_FO2816 | 260 | 1.000 | \varphi_{0}, P_{\nu} | | |
| cardona-qft-methods_FO2817 | 260 | 1.000 | \varphi_{0}-\partial_{\nu} \varphi_{0} | | |
| cardona-qft-methods_FO2818 | 260 | 1.000 | \partial \wedge \partial=0 | | |
| cardona-qft-methods_FO2819 | 261 | 1.000 | { }^{14-17} | | |
| cardona-qft-methods_FO2820 | 261 | 0.997 | V_{S T A T} | | |
| cardona-qft-methods_FO2821 | 261 | 1.000 | \left|x_{1}, x_{2}\right\rangle | | |
| cardona-qft-methods_FO2822 | 261 | 1.000 | O^{16}\left(C^{12}\right) | | |
| cardona-qft-methods_FO2823 | 261 | 1.000 | \tilde{O}^{16}\left(\tilde{C}^{12}\right) | | |
| cardona-qft-methods_FO2824 | 261 | 1.000 | 1 S_{1 / 2} | | |
| cardona-qft-methods_FO2825 | 261 | 1.000 | 10^{27} | | |
| cardona-qft-methods_FO2826 | 261 | 1.000 | 10^{-25} | | |
| cardona-qft-methods_FO2827 | 261 | 1.000 | \phi_{\theta} | | |
| cardona-qft-methods_FO2828 | 262 | 1.000 | \rho_{\theta}, \eta_{\theta} | | |
| cardona-qft-methods_FO2829 | 262 | 1.000 | \omega_{\beta} | | |
| cardona-qft-methods_FO2830 | 262 | 1.000 | H_{I} | | |
| cardona-qft-methods_FO2831 | 262 | 1.000 | x \sim y | | |
| cardona-qft-methods_FO2832 | 263 | 1.000 | S^{(2)} | | |
| cardona-qft-methods_FO2833 | 263 | 0.998 | \vec{P}_{\text {inc }} | | |
| cardona-qft-methods_FO2834 | 263 | 1.000 | \theta_{0 i} | | |
| cardona-qft-methods_FO2835 | 263 | 0.866 | { }_{0 i}\left(\vec{P}_{\text {inc }}\right)_{i} | | |
| cardona-qft-methods_FO2836 | 263 | 1.000 | Z^{0} \rightarrow 2 \gamma | | |
| cardona-qft-methods_FO2837 | 264 | 1.000 | a_{l m} | | |
| cardona-qft-methods_FO2838 | 264 | 1.000 | \Phi | | |
| cardona-qft-methods_FO2839 | 264 | 1.000 | \Delta_{l}^{T}(k) | | |
| cardona-qft-methods_FO2840 | 264 | 1.000 | \vec{\theta}^{0}=\theta(0,0,1) . P_{\Phi} | | |
| cardona-qft-methods_FO2841 | 264 | 1.000 | \left\langle a_{l m} a_{l^{\prime} m^{\prime}}^{*}\right\rangle_{\theta} | | |
| cardona-qft-methods_FO2842 | 264 | 1.000 | C M B | | |
| cardona-qft-methods_FO2843 | 264 | 1.000 | \sqrt{\theta} \leq 10^{-32} | | |
| cardona-qft-methods_FO2844 | 264 | 1.000 | \geq 10^{16} \mathrm{GeV} | | |
| cardona-qft-methods_FO2845 | 264 | 1.000 | x_{1} \sim | | |
| cardona-qft-methods_FO2846 | 264 | 1.000 | x_{2} | | |
| cardona-qft-methods_FO2847 | 267 | 1.000 | 5+5=10 | | |
| cardona-qft-methods_FO2848 | 267 | 0.998 | A d S_{5} \times S^{5} | | |
| cardona-qft-methods_FO2849 | 267 | 1.000 | A d S_{5} | | |
| cardona-qft-methods_FO2850 | 267 | 1.000 | S^{5} | | |
| cardona-qft-methods_FO2851 | 267 | 1.000 | A d S | | |
| cardona-qft-methods_FO2852 | 267 | 1.000 | C F T_{4} | | |
| cardona-qft-methods_FO2853 | 268 | 1.000 | X X X | | |
| cardona-qft-methods_FO2854 | 268 | 1.000 | I I B | | |
| cardona-qft-methods_FO2855 | 268 | 1.000 | \frac{1}{2} | | |
| cardona-qft-methods_FO2856 | 268 | 1.000 | \mathbb{C}^{2} | | |
| cardona-qft-methods_FO2857 | 268 | 1.000 | \vec{S} | | |
| cardona-qft-methods_FO2858 | 268 | 1.000 | \mathfrak{s u}(2) | | |
| cardona-qft-methods_FO2859 | 269 | 1.000 | s=\frac{1}{2} | | |
| cardona-qft-methods_FO2860 | 269 | 1.000 | \sigma^{3} | | |
| cardona-qft-methods_FO2861 | 270 | 1.000 | S^{+} | | |
| cardona-qft-methods_FO2862 | 270 | 1.000 | S^{-} | | |
| cardona-qft-methods_FO2863 | 270 | 1.000 | 2^{L} | | |
| cardona-qft-methods_FO2864 | 270 | 1.000 | L=2 | | |
| cardona-qft-methods_FO2865 | 270 | 1.000 | \mathbb{C}^{2} \otimes \mathbb{C}^{2} | | |
| cardona-qft-methods_FO2866 | 271 | 1.000 | L(L \sim 10) | | |
| cardona-qft-methods_FO2867 | 271 | 1.000 | 2^{L} \times 2^{L} | | |
| cardona-qft-methods_FO2868 | 271 | 0.873 | l^{\text {th }} | | |
| cardona-qft-methods_FO2869 | 271 | 0.873 | l+1^{\text {th }} | | |
| cardona-qft-methods_FO2870 | 271 | 0.953 | \vec{S}_{\text {tot }} | | |
| cardona-qft-methods_FO2871 | 271 | 0.953 | \vec{S}_{\text {tot }}=\sum_{l=1}^{L} \vec{S}_{l} | | |
| cardona-qft-methods_FO2872 | 271 | 0.953 | \vec{S}_{l} | | |
| cardona-qft-methods_FO2873 | 272 | 0.985 | L+1 | | |
| cardona-qft-methods_FO2874 | 272 | 0.985 | \binom{L}{M} \times\binom{ L}{M} | | |
| cardona-qft-methods_FO2875 | 272 | 1.000 | [\hat{H}, \hat{U}]=0 | | |
| cardona-qft-methods_FO2876 | 272 | 1.000 | \hat{U} | | |
| cardona-qft-methods_FO2877 | 272 | 1.000 | n=0,1, \ldots, L-1 | | |
| cardona-qft-methods_FO2878 | 272 | 1.000 | u_{k} | | |
| cardona-qft-methods_FO2879 | 273 | 0.883 | l_{i} | | |
| cardona-qft-methods_FO2880 | 273 | 0.883 | |0\rangle=|\uparrow \cdots \uparrow\rangle | | |
| cardona-qft-methods_FO2881 | 273 | 1.000 | S_{n} | | |
| cardona-qft-methods_FO2882 | 273 | 1.000 | A(\tau) | | |
| cardona-qft-methods_FO2883 | 273 | 1.000 | \operatorname{sgn}(\tau) | | |
| cardona-qft-methods_FO2884 | 274 | 1.000 | \mathbb{C}^{2} \otimes \mathbb{C}^{2} \otimes \mathbb{C}^{2} | | |
| cardona-qft-methods_FO2885 | 274 | 0.999 | L_{a, l}(u)=R_{a, l}\left(u-\frac{i}{2}\right) | | |
| cardona-qft-methods_FO2886 | 274 | 0.876 | 8 \times 8 | | |
| cardona-qft-methods_FO2887 | 275 | 1.000 | \left(\mathbb{C}^{2}\right)^{\otimes L} | | |
| cardona-qft-methods_FO2888 | 275 | 1.000 | 1, \ldots, L | | |
| cardona-qft-methods_FO2889 | 275 | 1.000 | 1,2, \ldots, L | | |
| cardona-qft-methods_FO2890 | 276 | 1.000 | R_{a, b}\left(u-u^{\prime}\right) | | |
| cardona-qft-methods_FO2891 | 276 | 1.000 | u=\frac{i}{2} | | |
| cardona-qft-methods_FO2892 | 276 | 1.000 | L_{a, l}\left(\frac{i}{2}\right)=i P_{a, l} | | |
| cardona-qft-methods_FO2893 | 276 | 1.000 | \hat{P} | | |
| cardona-qft-methods_FO2894 | 276 | 1.000 | \left[\hat{T}(u), \hat{T}\left(u^{\prime}\right)\right]=0 | | |
| cardona-qft-methods_FO2895 | 276 | 1.000 | \left\{\hat{Q}_{n}\right\} | | |
| cardona-qft-methods_FO2896 | 277 | 1.000 | \hat{H}|\psi\rangle=E|\psi\rangle | | |
| cardona-qft-methods_FO2897 | 277 | 1.000 | |\psi\rangle | | |
| cardona-qft-methods_FO2898 | 277 | 1.000 | \hat{A}(u), \hat{B}(u), \hat{C}(u) | | |
| cardona-qft-methods_FO2899 | 277 | 1.000 | \hat{D}(u) | | |
| cardona-qft-methods_FO2900 | 277 | 1.000 | \hat{C}(u)|0\rangle=0 | | |
| cardona-qft-methods_FO2901 | 277 | 0.960 | \left\{u_{k}\right\} | | |
| cardona-qft-methods_FO2902 | 277 | 1.000 | \hat{T}(u) | | |
| cardona-qft-methods_FO2903 | 277 | 0.894 | T(u) | | |
| cardona-qft-methods_FO2904 | 277 | 1.000 | u=u_{k} | | |
| cardona-qft-methods_FO2905 | 277 | 1.000 | \operatorname{res}_{u=u_{k}} T(u)=0 | | |
| cardona-qft-methods_FO2906 | 278 | 0.706 | T Q | | |
| cardona-qft-methods_FO2907 | 278 | 1.000 | \operatorname{SU}(N) | | |
| cardona-qft-methods_FO2908 | 278 | 1.000 | \beta | | |
| cardona-qft-methods_FO2909 | 278 | 1.000 | Y_{\mu}=\sum_{a=1}^{\left(N^{2}-1\right)} Y_{\mu}^{a} T_{a} | | |
| cardona-qft-methods_FO2910 | 278 | 1.000 | \mu \in\{0,1,2,3\} | | |
| cardona-qft-methods_FO2911 | 278 | 1.000 | T_{a} | | |
| cardona-qft-methods_FO2912 | 278 | 1.000 | N \times N | | |
| cardona-qft-methods_FO2913 | 278 | 1.000 | \left[T_{a}, T_{b}\right]=i f_{a b c} T_{c} | | |
| cardona-qft-methods_FO2914 | 278 | 0.954 | Y \rightarrow U Y U^{-1} | | |
| cardona-qft-methods_FO2915 | 278 | 0.954 | U \equiv U(x) \in \operatorname{SU}(N) | | |
| cardona-qft-methods_FO2916 | 279 | 1.000 | x \in \mathbb{R}^{1,3} | | |
| cardona-qft-methods_FO2917 | 279 | 1.000 | A_{\mu} \rightarrow U A_{\mu} U^{-1}-i\left(\partial_{\mu} U\right) | | |
| cardona-qft-methods_FO2918 | 279 | 1.000 | U^{-1} | | |
| cardona-qft-methods_FO2919 | 279 | 1.000 | \varphi_{m} | | |
| cardona-qft-methods_FO2920 | 279 | 1.000 | m \in\{1, \ldots, 6\} | | |
| cardona-qft-methods_FO2921 | 279 | 1.000 | \Delta_{0}=1 | | |
| cardona-qft-methods_FO2922 | 279 | 1.000 | X=\varphi_{1}+i \varphi_{2}, Y=\varphi_{3}+i \varphi_{4}, Z=\varphi_{5}+i \varphi_{6} | | |
| cardona-qft-methods_FO2923 | 279 | 1.000 | \bar{X}, \bar{Y}, \bar{Z} | | |
| cardona-qft-methods_FO2924 | 279 | 1.000 | \varphi_{a b} | | |
| cardona-qft-methods_FO2925 | 279 | 1.000 | a, b \in\{1, \ldots, \mathcal{N}=4\} | | |
| cardona-qft-methods_FO2926 | 279 | 1.000 | \psi_{a \alpha} | | |
| cardona-qft-methods_FO2927 | 279 | 1.000 | \bar{\psi}_{\dot{\alpha}}^{a} | | |
| cardona-qft-methods_FO2928 | 279 | 1.000 | a \in | | |
| cardona-qft-methods_FO2929 | 279 | 1.000 | \{1, \ldots \mathcal{N}=4\} | | |
| cardona-qft-methods_FO2930 | 279 | 1.000 | \dot{\alpha} | | |
| cardona-qft-methods_FO2931 | 279 | 0.993 | \alpha \in\{1,2\} | | |
| cardona-qft-methods_FO2932 | 279 | 0.993 | \mathfrak{s u}_{L}(2) | | |
| cardona-qft-methods_FO2933 | 279 | 1.000 | \dot{\alpha} \in\{\dot{1}, \dot{2}\} | | |
| cardona-qft-methods_FO2934 | 279 | 1.000 | \mathfrak{s u}_{R}(2) | | |
| cardona-qft-methods_FO2935 | 279 | 1.000 | \mathfrak{s o}(1,3) \simeq | | |
| cardona-qft-methods_FO2936 | 279 | 1.000 | \mathfrak{s} \mathfrak{u}_{L}(2) \oplus \mathfrak{s} \mathfrak{u}_{R}(2) | | |
| cardona-qft-methods_FO2937 | 279 | 1.000 | \Delta_{0}=3 / 2 | | |
| cardona-qft-methods_FO2938 | 279 | 1.000 | F_{\mu \nu}=i\left[D_{\mu}, D_{\nu}\right]=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu}-i\left[A_{\mu}, A_{\nu}\right] | | |
| cardona-qft-methods_FO2939 | 279 | 1.000 | D_{\mu}=\partial_{\mu}-i A_{\mu} | | |
| cardona-qft-methods_FO2940 | 279 | 1.000 | \Delta_{0}=2 | | |
| cardona-qft-methods_FO2941 | 279 | 1.000 | D_{\mu} \star=\partial_{\mu} \star-i\left[A_{\mu}, \star\right] | | |
| cardona-qft-methods_FO2942 | 279 | 1.000 | \lambda=N g_{Y M}^{2} | | |
| cardona-qft-methods_FO2943 | 279 | 1.000 | \left(\Sigma_{m}\right)^{a b} | | |
| cardona-qft-methods_FO2944 | 279 | 0.523 | \left(\sigma_{\mu}\right)^{\alpha \dot{\beta}} | | |
| cardona-qft-methods_FO2945 | 279 | 1.000 | N^{-1} | | |
| cardona-qft-methods_FO2946 | 280 | 1.000 | N \rightarrow \infty, g_{Y M} \rightarrow 0 | | |
| cardona-qft-methods_FO2947 | 280 | 1.000 | Y_{\mu}^{i j}=Y_{\mu}^{a}\left(T_{a}\right)^{i j} | | |
| cardona-qft-methods_FO2948 | 280 | 1.000 | i, j \in\{1,2, \ldots, N\} | | |
| cardona-qft-methods_FO2949 | 280 | 0.878 | \mathfrak{\mathfrak { s l }}(2, \mathbb{C}) \simeq \mathfrak{s o}(1,3) | | |
| cardona-qft-methods_FO2950 | 280 | 1.000 | M_{\mu \nu} | | |
| cardona-qft-methods_FO2951 | 280 | 1.000 | \partial_{\mu} \rightarrow D_{\mu} | | |
| cardona-qft-methods_FO2952 | 280 | 1.000 | P_{\mu}=i D_{\mu} | | |
| cardona-qft-methods_FO2953 | 280 | 1.000 | \left(M_{\mu \nu}, P_{\rho}\right) | | |
| cardona-qft-methods_FO2954 | 280 | 1.000 | \eta_{\mu \nu}=\operatorname{diag}(1,-1,-1,-1) | | |
| cardona-qft-methods_FO2955 | 280 | 1.000 | K_{\mu} | | |
| cardona-qft-methods_FO2956 | 280 | 1.000 | I: x_{\mu} \rightarrow x_{\mu} / x^{2} | | |
| cardona-qft-methods_FO2957 | 280 | 1.000 | K_{\mu}=I P_{\mu} I | | |
| cardona-qft-methods_FO2958 | 281 | 1.000 | 6+4+4+1=15 | | |
| cardona-qft-methods_FO2959 | 281 | 1.000 | \mathfrak{s o}(2,4) \simeq \mathfrak{s u}(2,2) | | |
| cardona-qft-methods_FO2960 | 281 | 1.000 | \mathfrak{s o}(6) | | |
| cardona-qft-methods_FO2961 | 281 | 0.998 | \mathfrak{s u}(4) | | |
| cardona-qft-methods_FO2962 | 281 | 0.907 | 2 \times 2 | | |
| cardona-qft-methods_FO2963 | 281 | 0.971 | \overline{\mathfrak{s u}}(2) | | |
| cardona-qft-methods_FO2966 | 281 | 0.733 | \bar{L} | | |
| cardona-qft-methods_FO2967 | 281 | 0.967 | \mathfrak{s u}(2,2) | | |
| cardona-qft-methods_FO2968 | 281 | 0.999 | \mathfrak{p s u}(2,2 \mid 4) | | |
| cardona-qft-methods_FO2970 | 282 | 1.000 | Q_{a \alpha} | | |
| cardona-qft-methods_FO2971 | 282 | 1.000 | \bar{Q}_{\dot{\alpha}}^{a} | | |
| cardona-qft-methods_FO2972 | 282 | 1.000 | a \in\{1, \ldots, \mathcal{N}=4\} | | |
| cardona-qft-methods_FO2973 | 282 | 1.000 | { }^{7,18,19} | | |
| cardona-qft-methods_FO2974 | 282 | 0.998 | \mathcal{N}=4 S Y M | | |
| cardona-qft-methods_FO2975 | 282 | 0.999 | \mathcal{O} | | |
| cardona-qft-methods_FO2976 | 282 | 1.000 | \Delta=\Delta_{0}+\gamma | | |
| cardona-qft-methods_FO2977 | 282 | 1.000 | \mathcal{O}(x) | | |
| cardona-qft-methods_FO2978 | 282 | 1.000 | \mathcal{N}= | | |
| cardona-qft-methods_FO2979 | 283 | 1.000 | N=\infty | | |
| cardona-qft-methods_FO2980 | 283 | 1.000 | \mathcal{O}= | | |
| cardona-qft-methods_FO2981 | 283 | 1.000 | \operatorname{Tr}\left(Z^{j}\right) | | |
| cardona-qft-methods_FO2982 | 283 | 1.000 | \left|\uparrow^{j}\right\rangle | | |
| cardona-qft-methods_FO2983 | 283 | 1.000 | \Delta_{0}=j | | |
| cardona-qft-methods_FO2984 | 283 | 1.000 | \gamma=0 | | |
| cardona-qft-methods_FO2985 | 283 | 1.000 | \mathcal{O}=\operatorname{Tr}\left(Z^{j-1} X\right) | | |
| cardona-qft-methods_FO2986 | 283 | 1.000 | \left|\uparrow^{j-1} \downarrow\right\rangle | | |
| cardona-qft-methods_FO2988 | 284 | 1.000 | A d s_{5} | | |
| cardona-qft-methods_FO2989 | 284 | 1.000 | S_{5} | | |
| cardona-qft-methods_FO2990 | 284 | 0.985 | (-,+,+,+,+,-) | | |
| cardona-qft-methods_FO2991 | 284 | 0.535 | (+,+,+,+,+,+) | | |
| cardona-qft-methods_FO2992 | 284 | 0.562 | A d S_{5}=\mathrm{SO}(4,2) / \mathrm{SO}(1,4) | | |
| cardona-qft-methods_FO2993 | 284 | 0.718 | S^{5}=\operatorname{SO}(6) / \operatorname{SO}(5) | | |
| cardona-qft-methods_FO2994 | 284 | 0.935 | \operatorname{PSU}(2,2 \mid 4) | | |
| cardona-qft-methods_FO2995 | 284 | 1.000 | M \in\{0,1, \ldots, 5\}, N \in\{1, \ldots, 6\} | | |
| cardona-qft-methods_FO2996 | 284 | 1.000 | 1 / \alpha^{\prime} | | |
| cardona-qft-methods_FO2997 | 284 | 0.918 | (+,+) | | |
| cardona-qft-methods_FO2998 | 284 | 0.918 | \partial_{0}=\partial_{\tau}, \partial_{1}=\partial_{\sigma} | | |
| cardona-qft-methods_FO2999 | 284 | 1.000 | \alpha^{\prime} | | |
| cardona-qft-methods_FO3000 | 284 | 0.999 | \alpha^{\prime} \rightarrow 0 | | |
| cardona-qft-methods_FO3001 | 285 | 0.848 | \mathcal{N}=4 \mathrm{SYM} | | |
| cardona-qft-methods_FO3002 | 285 | 1.000 | { }^{3,4} | | |
| cardona-qft-methods_FO3003 | 285 | 0.996 | \lambda=g_{\mathrm{YM}} N^{2} | | |
| cardona-qft-methods_FO3004 | 285 | 0.996 | N-1 | | |
| cardona-qft-methods_FO3005 | 285 | 0.915 | g_{\mathrm{YM}} | | |
| cardona-qft-methods_FO3006 | 285 | 1.000 | g_{\mathrm{s}} | | |
| cardona-qft-methods_FO3007 | 285 | 1.000 | N \rightarrow \infty | | |
| cardona-qft-methods_FO3008 | 285 | 1.000 | g_{\mathrm{s}} \rightarrow 0 | | |
| cardona-qft-methods_FO3009 | 286 | 1.000 | \phi_{1}, \phi_{2}, \phi_{3} | | |
| cardona-qft-methods_FO3010 | 286 | 1.000 | J_{1}, J_{2}, J_{3} | | |
| cardona-qft-methods_FO3011 | 286 | 0.852 | \mathfrak{s} \mathfrak{o}(6) \simeq \mathfrak{s} \mathfrak{u}(4) | | |
| cardona-qft-methods_FO3012 | 286 | 1.000 | t, \alpha_{1}, \alpha_{2} | | |
| cardona-qft-methods_FO3013 | 286 | 1.000 | S_{1} | | |
| cardona-qft-methods_FO3014 | 286 | 1.000 | \mathfrak{s o}(2,4) \simeq | | |
| cardona-qft-methods_FO3016 | 286 | 0.954 | 30 \mid 32 | | |
| cardona-qft-methods_FO3018 | 287 | 1.000 | 8_{B}+8_{F} | | |
| cardona-qft-methods_FO3020 | 287 | 1.000 | \dot{A} | | |
| cardona-qft-methods_FO3021 | 287 | 1.000 | \bar{Z} \sim X \bar{X}+Y \bar{Y} | | |
| cardona-qft-methods_FO3022 | 287 | 1.000 | F \sim D D | | |
| cardona-qft-methods_FO3023 | 288 | 1.000 | \mathrm{AdS}_{5} \times \mathrm{S}^{5} | | |
| cardona-qft-methods_FO3024 | 289 | 0.747 | \left.\mathrm{ple}^{1}-{ }^{4}\right) | | |
| cardona-qft-methods_FO3025 | 290 | 1.000 | (2,0) | | |
| cardona-qft-methods_FO3026 | 290 | 0.991 | { }^{5}-{ }^{7} | | |
| cardona-qft-methods_FO3027 | 290 | 0.422 | { }^{8}-,^{13} | | |
| cardona-qft-methods_FO3028 | 291 | 0.502 | { }^{19-}{ }^{21} | | |
| cardona-qft-methods_FO3029 | 292 | 0.999 | (0 \leq \sigma \leq \pi | | |
| cardona-qft-methods_FO3030 | 292 | 1.000 | 0 \leq \sigma \leq 2 \pi | | |
| cardona-qft-methods_FO3031 | 292 | 1.000 | 2 \pi | | |
| cardona-qft-methods_FO3032 | 292 | 1.000 | M=0, \ldots, D-1 ; \alpha=\tau, \sigma | | |
| cardona-qft-methods_FO3033 | 292 | 1.000 | X^{M} | | |
| cardona-qft-methods_FO3035 | 292 | 1.000 | \gamma^{\alpha \beta} | | |
| cardona-qft-methods_FO3036 | 292 | 1.000 | \eta_{M N} | | |
| cardona-qft-methods_FO3037 | 293 | 1.000 | l_{s} | | |
| cardona-qft-methods_FO3038 | 293 | 0.999 | M_{s} | | |
| cardona-qft-methods_FO3039 | 293 | 0.999 | c=\hbar=1 | | |
| cardona-qft-methods_FO3040 | 293 | 1.000 | \hbar / c | | |
| cardona-qft-methods_FO3041 | 293 | 1.000 | \sigma^{ \pm}=\tau \pm \sigma | | |
| cardona-qft-methods_FO3042 | 293 | 0.999 | X^{M}(\tau, 0)=X^{M}(\tau, 2 \pi), X^{\prime M}(\tau, 0)=X^{\prime M}(\tau, 2 \pi) | | |
| cardona-qft-methods_FO3043 | 293 | 1.000 | x^{M} | | |
| cardona-qft-methods_FO3044 | 293 | 1.000 | p^{M} | | |
| cardona-qft-methods_FO3045 | 293 | 1.000 | \alpha_{-n}^{M}=\left(\alpha_{n}^{M}\right)^{*} | | |
| cardona-qft-methods_FO3046 | 293 | 1.000 | \tilde{\alpha}_{-n}^{M}=\left(\tilde{\alpha}_{n}^{M}\right)^{*} | | |
| cardona-qft-methods_FO3047 | 293 | 1.000 | \gamma_{\alpha \beta} | | |
| cardona-qft-methods_FO3048 | 294 | 1.000 | \alpha_{n}^{M}, \tilde{\alpha}_{n}^{M} | | |
| cardona-qft-methods_FO3049 | 294 | 1.000 | \alpha_{-n}^{M}, \tilde{\alpha}_{-n}^{M} | | |
| cardona-qft-methods_FO3050 | 294 | 0.890 | \mathrm{in}^{1}-{ }^{3} | | |
| cardona-qft-methods_FO3051 | 294 | 1.000 | N=\tilde{N} | | |
| cardona-qft-methods_FO3052 | 294 | 1.000 | N, \tilde{N} | | |
| cardona-qft-methods_FO3053 | 294 | 1.000 | k^{M}, k \cdot k=0 | | |
| cardona-qft-methods_FO3054 | 294 | 1.000 | \xi, \tilde{\xi} | | |
| cardona-qft-methods_FO3055 | 294 | 1.000 | \xi \cdot k=\tilde{\xi} \cdot k=0 | | |
| cardona-qft-methods_FO3056 | 294 | 0.999 | \vec{k}=(k, k, 0, \ldots, 0) | | |
| cardona-qft-methods_FO3057 | 294 | 0.999 | \xi_{M}, \tilde{\xi}_{M} | | |
| cardona-qft-methods_FO3058 | 294 | 0.999 | 2, \ldots, D-1 | | |
| cardona-qft-methods_FO3059 | 294 | 0.987 | \operatorname{SO}(D-2) | | |
| cardona-qft-methods_FO3060 | 294 | 0.987 | \xi_{M N} \equiv \xi_{M} \tilde{\xi}_{N} | | |
| cardona-qft-methods_FO3061 | 295 | 1.000 | \xi_{M N} | | |
| cardona-qft-methods_FO3062 | 295 | 1.000 | \xi_{t} | | |
| cardona-qft-methods_FO3063 | 295 | 0.968 | -\frac{4}{\alpha^{\prime}} | | |
| cardona-qft-methods_FO3064 | 295 | 1.000 | G_{M N}(X) | | |
| cardona-qft-methods_FO3065 | 295 | 1.000 | G_{M N}= | | |
| cardona-qft-methods_FO3066 | 295 | 1.000 | \eta_{M N}+h_{M N}(X) | | |
| cardona-qft-methods_FO3067 | 295 | 1.000 | h_{M N} \propto \xi_{M N}^{s} | | |
| cardona-qft-methods_FO3068 | 296 | 1.000 | \hbar | | |
| cardona-qft-methods_FO3069 | 296 | 0.986 | e^{-\Phi \chi} | | |
| cardona-qft-methods_FO3070 | 296 | 1.000 | \chi=2-2 h-b-c | | |
| cardona-qft-methods_FO3071 | 296 | 1.000 | \delta \chi=-2 | | |
| cardona-qft-methods_FO3072 | 296 | 1.000 | e^{2 \Phi} | | |
| cardona-qft-methods_FO3073 | 296 | 0.992 | g_{s}=e^{\langle\Phi\rangle} | | |
| cardona-qft-methods_FO3074 | 296 | 1.000 | \left(1 / \sqrt{\alpha^{\prime}}\right) | | |
| cardona-qft-methods_FO3075 | 297 | 1.000 | H_{M P Q} | | |
| cardona-qft-methods_FO3076 | 297 | 1.000 | B_{P Q} | | |
| cardona-qft-methods_FO3077 | 297 | 1.000 | H_{M P Q}=\partial_{[M} B_{P Q]} | | |
| cardona-qft-methods_FO3078 | 297 | 1.000 | 1 / \sqrt{\alpha^{\prime}} | | |
| cardona-qft-methods_FO3079 | 297 | 1.000 | D \neq 26 | | |
| cardona-qft-methods_FO3080 | 297 | 0.992 | \left.\Phi=V_{M} X^{M},|V|^{2}=(D-26) / \alpha^{\prime}\right) | | |
| cardona-qft-methods_FO3081 | 298 | 1.000 | \sigma=0, \pi | | |
| cardona-qft-methods_FO3082 | 298 | 1.000 | \partial_{\sigma} X^{M}(\tau, 0)=\partial_{\sigma} X^{M}(\tau, \pi)=0 | | |
| cardona-qft-methods_FO3083 | 298 | 1.000 | A_{M} | | |
| cardona-qft-methods_FO3084 | 298 | 1.000 | F=d A | | |
| cardona-qft-methods_FO3085 | 298 | 1.000 | g_{o}=e^{\Phi / 2} | | |
| cardona-qft-methods_FO3086 | 298 | 1.000 | g_{s} | | |
| cardona-qft-methods_FO3087 | 298 | 0.997 | p+1 | | |
| cardona-qft-methods_FO3088 | 298 | 0.997 | \mathrm{D} p | | |
| cardona-qft-methods_FO3089 | 298 | 0.829 | D-p-1 | | |
| cardona-qft-methods_FO3090 | 298 | 1.000 | U(n) | | |
| cardona-qft-methods_FO3091 | 299 | 1.000 | \Psi^{M} | | |
| cardona-qft-methods_FO3092 | 299 | 1.000 | \tilde{\Psi}^{M} | | |
| cardona-qft-methods_FO3093 | 299 | 1.000 | D-2 | | |
| cardona-qft-methods_FO3094 | 299 | 0.947 | \Psi^{M}, \tilde{\Psi}^{M} | | |
| cardona-qft-methods_FO3095 | 299 | 1.000 | \tau \rightarrow \mathrm{i} \tau | | |
| cardona-qft-methods_FO3096 | 299 | 1.000 | z=e^{\tau-\mathrm{i} \sigma} | | |
| cardona-qft-methods_FO3097 | 299 | 0.514 | \tilde{\Psi} | | |
| cardona-qft-methods_FO3098 | 299 | 0.997 | \tilde{\psi} | | |
| cardona-qft-methods_FO3099 | 299 | 1.000 | D=10 | | |
| cardona-qft-methods_FO3100 | 300 | 1.000 | \xi_{M} | | |
| cardona-qft-methods_FO3101 | 300 | 1.000 | \vec{k} | | |
| cardona-qft-methods_FO3102 | 300 | 0.850 | \mathrm{SO}(8) | | |
| cardona-qft-methods_FO3103 | 300 | 1.000 | \Psi_{0} | | |
| cardona-qft-methods_FO3104 | 300 | 1.000 | d_{ \pm}^{i}=\frac{1}{\sqrt{2}}\left(\psi_{0}^{2 i} \pm \psi_{0}^{2 i+1}\right) | | |
| cardona-qft-methods_FO3105 | 300 | 1.000 | i=1, . ., 4 | | |
| cardona-qft-methods_FO3106 | 300 | 0.922 | \pm \frac{1}{2} | | |
| cardona-qft-methods_FO3107 | 300 | 0.922 | i .{ }^{\text {c }} | | |
| cardona-qft-methods_FO3108 | 300 | 0.994 | \psi_{0}^{M}|0\rangle | | |
| cardona-qft-methods_FO3109 | 300 | 1.000 | \mathbf{8}_{s} \oplus \mathbf{8}_{c} | | |
| cardona-qft-methods_FO3110 | 300 | 1.000 | 8 X^{M} | | |
| cardona-qft-methods_FO3111 | 300 | 1.000 | \sum_{i=1}^{4} s_{i}=0(\bmod 2) | | |
| cardona-qft-methods_FO3112 | 300 | 0.996 | \xi_{M N} \psi_{0}^{M} \tilde{\psi}_{0}^{N}|0\rangle | | |
| cardona-qft-methods_FO3113 | 300 | 0.996 | |s\rangle \otimes|\tilde{s}\rangle | | |
| cardona-qft-methods_FO3114 | 301 | 1.000 | \mathbf{8}_{s} | | |
| cardona-qft-methods_FO3115 | 301 | 1.000 | \mathbf{8}_{c} | | |
| cardona-qft-methods_FO3116 | 301 | 0.996 | \mathbf{8}_{v} | | |
| cardona-qft-methods_FO3117 | 301 | 0.998 | \mathbf{8}_{s}, \mathbf{8}_{c}, \mathbf{8}_{v} | | |
| cardona-qft-methods_FO3118 | 301 | 0.993 | C_{n} | | |
| cardona-qft-methods_FO3119 | 301 | 1.000 | C_{4} | | |
| cardona-qft-methods_FO3120 | 301 | 1.000 | d C_{4}=* d C_{4} | | |
| cardona-qft-methods_FO3121 | 301 | 0.988 | \lambda^{A}(\mathrm{~A}=1,2) | | |
| cardona-qft-methods_FO3122 | 301 | 0.984 | \mathbf{5 6}, \Psi^{A, M} | | |
| cardona-qft-methods_FO3123 | 302 | 1.000 | S^{1} | | |
| cardona-qft-methods_FO3124 | 302 | 1.000 | 1 / R | | |
| cardona-qft-methods_FO3125 | 302 | 1.000 | X^{M}(\tau, 2 \pi)= | | |
| cardona-qft-methods_FO3126 | 302 | 1.000 | X^{M}(\tau, 0)+2 \pi m R | | |
| cardona-qft-methods_FO3127 | 302 | 0.943 | \alpha^{\prime} / R! | | |
| cardona-qft-methods_FO3128 | 303 | 1.000 | X_{L}^{M}+X_{R}^{M} | | |
| cardona-qft-methods_FO3129 | 303 | 1.000 | X_{L}^{M}-X_{R}^{M} | | |
| cardona-qft-methods_FO3130 | 303 | 0.978 | \psi^{M} | | |
| cardona-qft-methods_FO3131 | 303 | 0.978 | \bar{\psi}^{M} | | |
| cardona-qft-methods_FO3132 | 303 | 1.000 | O(n, n, \mathbb{Z}) | | |
| cardona-qft-methods_FO3133 | 303 | 1.000 | O(8,8) | | |
| cardona-qft-methods_FO3134 | 303 | 0.960 | G l(8) | | |
| cardona-qft-methods_FO3135 | 303 | 1.000 | O(8) | | |
| cardona-qft-methods_FO3136 | 303 | 1.000 | { }^{\text {e }} | | |
| cardona-qft-methods_FO3137 | 303 | 0.995 | \mathrm{D}(p \pm 1) | | |
| cardona-qft-methods_FO3138 | 303 | 1.000 | O(10,10) | | |
| cardona-qft-methods_FO3139 | 304 | 0.998 | T_{p}=8 \pi^{7} \alpha^{\prime 7 / 2}\left(4 \pi^{2} \alpha^{\prime}\right)^{-p / 2} | | |
| cardona-qft-methods_FO3140 | 304 | 0.989 | S U(3) \times S U(2) \times | | |
| cardona-qft-methods_FO3141 | 305 | 1.000 | O(n, n) | | |
| cardona-qft-methods_FO3142 | 305 | 1.000 | { }^{19,20} | | |
| cardona-qft-methods_FO3143 | 305 | 1.000 | { }^{22,23} | | |
| cardona-qft-methods_FO3144 | 305 | 0.998 | T^{*} | | |
| cardona-qft-methods_FO3145 | 305 | 1.000 | T \oplus T^{*} | | |
| cardona-qft-methods_FO3146 | 305 | 1.000 | X+\zeta | | |
| cardona-qft-methods_FO3147 | 306 | 1.000 | n=6 | | |
| cardona-qft-methods_FO3148 | 306 | 1.000 | O(6,6) | | |
| cardona-qft-methods_FO3149 | 306 | 1.000 | U_{\alpha} | | |
| cardona-qft-methods_FO3150 | 306 | 1.000 | U_{\beta} | | |
| cardona-qft-methods_FO3151 | 306 | 0.460 | \mathrm{Gl}(6) | | |
| cardona-qft-methods_FO3152 | 306 | 0.460 | a_{(\alpha \beta)} | | |
| cardona-qft-methods_FO3153 | 306 | 0.998 | b_{(\alpha \beta)} | | |
| cardona-qft-methods_FO3154 | 306 | 1.000 | a^{-T}=\left(a^{-1}\right)^{T} | | |
| cardona-qft-methods_FO3155 | 306 | 1.000 | b_{(\alpha \beta)}=-\mathrm{d} \Lambda_{(\alpha \beta)} | | |
| cardona-qft-methods_FO3156 | 306 | 1.000 | \Lambda_{(\alpha \beta)} | | |
| cardona-qft-methods_FO3157 | 306 | 1.000 | U_{\alpha} \cap U_{\beta} \cap U_{\gamma} | | |
| cardona-qft-methods_FO3158 | 306 | 1.000 | g_{\alpha \beta \gamma}:=\mathrm{i} \alpha | | |
| cardona-qft-methods_FO3159 | 306 | 1.000 | \mathcal{J} | | |
| cardona-qft-methods_FO3160 | 306 | 1.000 | -\mathbb{I}_{2 d} | | |
| cardona-qft-methods_FO3161 | 306 | 1.000 | I_{m}{ }^{n} | | |
| cardona-qft-methods_FO3162 | 306 | 1.000 | -\mathbb{I}_{d} | | |
| cardona-qft-methods_FO3163 | 306 | 1.000 | \mathcal{J}^{t} \mathcal{G} \mathcal{J}=\mathcal{G} | | |
| cardona-qft-methods_FO3164 | 306 | 1.000 | \mathcal{G} | | |
| cardona-qft-methods_FO3165 | 307 | 1.000 | I^{2}=-\mathbb{I}_{d} | | |
| cardona-qft-methods_FO3166 | 307 | 1.000 | \mathcal{J}^{2}=-\mathbb{I}_{2 d}, \mathcal{J}^{t} \mathcal{G} \mathcal{J}=\mathcal{G} | | |
| cardona-qft-methods_FO3167 | 307 | 1.000 | J_{m n} | | |
| cardona-qft-methods_FO3168 | 307 | 1.000 | \pi_{ \pm}=\frac{1}{2}\left(\mathbb{I}_{d} \pm \mathrm{i} I\right) | | |
| cardona-qft-methods_FO3169 | 307 | 1.000 | \Pi_{ \pm}= | | |
| cardona-qft-methods_FO3170 | 307 | 1.000 | \frac{1}{2}\left(\mathbb{I}_{2 d} \pm \mathrm{i} \mathcal{J}\right) | | |
| cardona-qft-methods_FO3171 | 307 | 0.999 | \pi_{\mp}\left[\pi_{ \pm} X, \pi_{ \pm} Y\right]=0 | | |
| cardona-qft-methods_FO3172 | 307 | 1.000 | \Pi | | |
| cardona-qft-methods_FO3173 | 307 | 1.000 | T M \oplus T^{*} M | | |
| cardona-qft-methods_FO3174 | 307 | 1.000 | \mathcal{J}_{1} | | |
| cardona-qft-methods_FO3175 | 307 | 1.000 | \mathcal{J}_{2} | | |
| cardona-qft-methods_FO3176 | 307 | 1.000 | d J=0 | | |
| cardona-qft-methods_FO3177 | 307 | 1.000 | \mathbb{C}^{k} \times\left(\mathbb{R}^{d-2 k}, J\right) | | |
| cardona-qft-methods_FO3178 | 307 | 1.000 | J=\mathrm{d} x^{2 k+1} \wedge \mathrm{~d} x^{2 k+2}+\ldots+\mathrm{d} x^{d-1} \wedge \mathrm{~d} x^{d} | | |
| cardona-qft-methods_FO3179 | 307 | 1.000 | k \leq d / 2 | | |
| cardona-qft-methods_FO3180 | 308 | 1.000 | \mathcal{J}_{i}, i=1,2 | | |
| cardona-qft-methods_FO3181 | 308 | 0.998 | \mathcal{J}_{i} | | |
| cardona-qft-methods_FO3182 | 308 | 1.000 | +i | | |
| cardona-qft-methods_FO3183 | 308 | 1.000 | \Phi_{ \pm} | | |
| cardona-qft-methods_FO3184 | 309 | 1.000 | e^{-B} \Phi= | | |
| cardona-qft-methods_FO3185 | 309 | 0.995 | \left(1-B \wedge+\frac{1}{2} B \wedge B \wedge+\ldots\right) \Phi | | |
| cardona-qft-methods_FO3186 | 309 | 1.000 | \Phi^{D} | | |
| cardona-qft-methods_FO3187 | 309 | 1.000 | \eta^{1}=\eta^{2} \equiv \eta | | |
| cardona-qft-methods_FO3188 | 309 | 1.000 | \eta | | |
| cardona-qft-methods_FO3189 | 309 | 1.000 | S O(6) | | |
| cardona-qft-methods_FO3190 | 309 | 0.891 | \mathbf{4} \rightarrow \mathbf{3}+\mathbf{1} | | |
| cardona-qft-methods_FO3191 | 309 | 0.985 | \mathbf{1 0}+\mathbf{1 0}^{*} | | |
| cardona-qft-methods_FO3192 | 309 | 0.649 | \operatorname{SU}(3) | | |
| cardona-qft-methods_FO3193 | 310 | 0.695 | (J, \rho) | | |
| cardona-qft-methods_FO3194 | 310 | 0.695 | \rho=\operatorname{Re} \Omega | | |
| cardona-qft-methods_FO3195 | 310 | 0.952 | \operatorname{GL}(6, \mathbb{R}) | | |
| cardona-qft-methods_FO3196 | 310 | 0.994 | \operatorname{Sp}(6, \mathbb{R}) | | |
| cardona-qft-methods_FO3197 | 310 | 0.585 | \operatorname{SL}(3, \mathbb{C}) | | |
| cardona-qft-methods_FO3198 | 310 | 0.997 | J \wedge \rho=0 | | |
| cardona-qft-methods_FO3199 | 310 | 0.997 | \operatorname{SU}(3) \subset \operatorname{SO}(6) | | |
| cardona-qft-methods_FO3200 | 310 | 0.999 | \eta^{2}=\left(v+\mathrm{i} v^{\prime}\right)_{m} \gamma^{m} \eta^{1} | | |
| cardona-qft-methods_FO3201 | 310 | 0.632 | \left(\eta^{1}, \eta^{2}\right) | | |
| cardona-qft-methods_FO3202 | 310 | 0.859 | (1,1) | | |
| cardona-qft-methods_FO3203 | 310 | 0.992 | v^{\prime} . \Phi_{+} | | |
| cardona-qft-methods_FO3204 | 310 | 1.000 | \Phi_{-} | | |
| cardona-qft-methods_FO3205 | 311 | 0.712 | \Leftrightarrow \exists | | |
| cardona-qft-methods_FO3206 | 311 | 0.712 | \mathrm{d} \Phi=(v\llcorner+\zeta \wedge) \Phi | | |
| cardona-qft-methods_FO3207 | 311 | 0.997 | \Leftrightarrow \exists \Phi | | |
| cardona-qft-methods_FO3208 | 311 | 0.997 | \mathrm{d} \Phi=0 | | |
| cardona-qft-methods_FO3209 | 311 | 1.000 | W_{5} | | |
| cardona-qft-methods_FO3210 | 311 | 1.000 | \exists f | | |
| cardona-qft-methods_FO3211 | 311 | 1.000 | \Phi=e^{-f} \Omega | | |
| cardona-qft-methods_FO3212 | 311 | 1.000 | d-H \wedge | | |
| cardona-qft-methods_FO3213 | 311 | 0.980 | \mathrm{d} \Phi^{D}=0 | | |
| cardona-qft-methods_FO3214 | 312 | 1.000 | \eta_{\mu \nu} | | |
| cardona-qft-methods_FO3215 | 312 | 0.840 | \left\langle Q_{\epsilon} \chi\right\rangle=\left\langle\delta_{\epsilon} \chi\right\rangle=0 | | |
| cardona-qft-methods_FO3216 | 313 | 0.703 | <\delta_{\epsilon} \chi>=0 | | |
| cardona-qft-methods_FO3217 | 313 | 1.000 | \psi_{M}^{A}, A=1,2 | | |
| cardona-qft-methods_FO3218 | 313 | 1.000 | \lambda^{A} | | |
| cardona-qft-methods_FO3219 | 313 | 1.000 | M=0, \ldots, 9, \psi_{M} | | |
| cardona-qft-methods_FO3220 | 313 | 1.000 | \psi_{M}= | | |
| cardona-qft-methods_FO3221 | 313 | 0.769 | \binom{\psi_{M}^{1}}{\psi_{M}^{2}} | | |
| cardona-qft-methods_FO3222 | 313 | 0.994 | \mathcal{P}_{n} | | |
| cardona-qft-methods_FO3223 | 313 | 0.994 | \mathcal{P}=\Gamma_{11} | | |
| cardona-qft-methods_FO3224 | 313 | 1.000 | \mathcal{P}_{n}=\Gamma_{11}^{(n / 2)} \sigma^{1} | | |
| cardona-qft-methods_FO3225 | 313 | 1.000 | \mathcal{P}=-\sigma^{3}, \mathcal{P}_{n}=\sigma^{1} | | |
| cardona-qft-methods_FO3226 | 313 | 1.000 | \frac{n+1}{2} | | |
| cardona-qft-methods_FO3227 | 313 | 1.000 | \mathcal{P}_{n}=\mathrm{i} \sigma^{2} | | |
| cardona-qft-methods_FO3228 | 313 | 0.670 | \mathscr{F}_{n}=\frac{1}{n!} F_{P_{1} \ldots P_{N}} \Gamma^{P_{1} \ldots P_{N}} | | |
| cardona-qft-methods_FO3229 | 313 | 0.670 | H_{M} \equiv \frac{1}{2} H_{M N P} \Gamma^{N P} | | |
| cardona-qft-methods_FO3230 | 313 | 0.919 | C_{1} \ldots C_{9} | | |
| cardona-qft-methods_FO3231 | 313 | 0.919 | C_{0}, C_{2} \ldots C_{10} | | |
| cardona-qft-methods_FO3232 | 313 | 1.000 | F^{(10)} | | |
| cardona-qft-methods_FO3233 | 313 | 1.000 | \hat{F}= | | |
| cardona-qft-methods_FO3234 | 313 | 0.999 | \mathrm{d} C+m e^{B} | | |
| cardona-qft-methods_FO3235 | 313 | 0.999 | m \equiv F_{0}^{(10)}=\hat{F}_{0} | | |
| cardona-qft-methods_FO3236 | 313 | 1.000 | S O(n) | | |
| cardona-qft-methods_FO3237 | 314 | 1.000 | \nabla_{M} \epsilon=0 | | |
| cardona-qft-methods_FO3238 | 314 | 0.998 | \Gamma^{\mu}=\gamma^{\mu} \otimes \mathbf{1}, \Gamma^{m}=\gamma_{5} \otimes \gamma^{m} | | |
| cardona-qft-methods_FO3239 | 314 | 1.000 | e^{2 A} \tilde{g}_{\mu \nu} | | |
| cardona-qft-methods_FO3240 | 314 | 0.968 | \gamma_{\mu \nu} | | |
| cardona-qft-methods_FO3241 | 314 | 0.968 | \nabla_{m} A \nabla^{m} A=0 | | |
| cardona-qft-methods_FO3242 | 314 | 0.998 | \gamma_{11} \epsilon_{\text {IIA }}^{1}=\epsilon_{\text {IIA }}^{1} | | |
| cardona-qft-methods_FO3243 | 314 | 0.998 | \gamma_{11} \epsilon_{\text {IIA }}^{2}=-\epsilon_{\text {IIA }}^{2} | | |
| cardona-qft-methods_FO3244 | 314 | 1.000 | \xi_{-}^{1,2}=\left(\xi_{+}^{1,2}\right)^{*} | | |
| cardona-qft-methods_FO3245 | 314 | 1.000 | \eta_{-}^{A}=\left(\eta_{+}^{A}\right)^{*} | | |
| cardona-qft-methods_FO3246 | 314 | 1.000 | \eta^{1}=\eta^{2} | | |
| cardona-qft-methods_FO3247 | 315 | 0.677 | \operatorname{Hol}(\nabla) \subseteq \operatorname{SU}(3) .^{\mathrm{h}} | | |
| cardona-qft-methods_FO3248 | 315 | 1.000 | \xi^{1} | | |
| cardona-qft-methods_FO3249 | 315 | 1.000 | \xi^{2} | | |
| cardona-qft-methods_FO3250 | 315 | 1.000 | \mathbb{N}=2 | | |
| cardona-qft-methods_FO3251 | 315 | 1.000 | \mathrm{K} 3 \times T^{2} | | |
| cardona-qft-methods_FO3252 | 315 | 1.000 | \mathbb{N}=4 | | |
| cardona-qft-methods_FO3253 | 315 | 1.000 | T^{6} | | |
| cardona-qft-methods_FO3254 | 315 | 0.826 | \mathbb{N}=8 | | |
| cardona-qft-methods_FO3255 | 315 | 1.000 | \mathbb{N}=1 | | |
| cardona-qft-methods_FO3256 | 315 | 1.000 | F_{n}, H_{3} | | |
| cardona-qft-methods_FO3257 | 316 | 1.000 | \mathcal{N}=2 | | |
| cardona-qft-methods_FO3258 | 316 | 1.000 | S O(d) | | |
| cardona-qft-methods_FO3259 | 317 | 1.000 | c_{1}=0 | | |
| cardona-qft-methods_FO3260 | 317 | 1.000 | \delta \Psi_{m}= | | |
| cardona-qft-methods_FO3261 | 317 | 1.000 | \delta \lambda=0 | | |
| cardona-qft-methods_FO3262 | 318 | 0.924 | \operatorname{SU}(3) \times \operatorname{SU}(3) | | |
| cardona-qft-methods_FO3263 | 318 | 1.000 | 6-2 k | | |
| cardona-qft-methods_FO3264 | 318 | 0.942 | (13,14) | | |
| cardona-qft-methods_FO3265 | 318 | 0.942 | \tilde{\Phi}_{ \pm}=\Phi_{ \pm}, F_{\text {IIA }}=F_{\text {IIB }}=A=0 .{ }^{36} | | |
| cardona-qft-methods_FO3266 | 318 | 1.000 | T^{6}, K 3 \times T^{2} | | |
| cardona-qft-methods_FO3267 | 318 | 1.000 | C Y_{3} | | |
| cardona-qft-methods_FO3268 | 318 | 0.999 | 2 h^{2,1} | | |
| cardona-qft-methods_FO3269 | 318 | 0.999 | h^{1,1} | | |
| cardona-qft-methods_FO3270 | 318 | 0.731 | (6,6) | | |
| cardona-qft-methods_FO3271 | 318 | 1.000 | { }^{\mathrm{i}} H | | |
| cardona-qft-methods_FO3272 | 318 | 1.000 | (d-H \wedge) \Omega=0 | | |
| cardona-qft-methods_FO3273 | 318 | 1.000 | d \Omega=0 | | |
| cardona-qft-methods_FO3274 | 322 | 1.000 | \mathrm{N}=(2,2) | | |
| cardona-qft-methods_FO3275 | 322 | 0.976 | \mathrm{D}=10 | | |
| cardona-qft-methods_FO3276 | 322 | 0.978 | \mathrm{N}=1 | | |
| cardona-qft-methods_FO3277 | 326 | 1.000 | (G, M) | | |
| cardona-qft-methods_FO3278 | 326 | 1.000 | (A, M) | | |
| cardona-qft-methods_FO3279 | 326 | 1.000 | A=T^{*} M | | |
| cardona-qft-methods_FO3280 | 327 | 1.000 | (M, \Pi) | | |
| cardona-qft-methods_FO3281 | 328 | 1.000 | { }^{2,5} | | |
| cardona-qft-methods_FO3282 | 328 | 1.000 | \Pi \in \Gamma(T M \wedge T M) | | |
| cardona-qft-methods_FO3283 | 328 | 1.000 | \{\}:, \mathcal{C}^{\infty}(M) \otimes \mathcal{C}^{\infty}(M) \rightarrow \mathcal{C}^{\infty}(M) | | |
| cardona-qft-methods_FO3284 | 329 | 1.000 | T \Sigma | | |
| cardona-qft-methods_FO3285 | 329 | 0.968 | (X, \eta) | | |
| cardona-qft-methods_FO3286 | 329 | 0.968 | \mathcal{C}^{k+1} | | |
| cardona-qft-methods_FO3287 | 329 | 1.000 | \eta \in \Gamma^{k}\left(\Sigma, T^{*} \Sigma \otimes X^{*} T^{*} M\right) | | |
| cardona-qft-methods_FO3288 | 329 | 1.000 | k \in\{0,1, \cdots\} | | |
| cardona-qft-methods_FO3289 | 329 | 1.000 | \Pi^{\#} | | |
| cardona-qft-methods_FO3290 | 329 | 1.000 | T^{*} M \rightarrow T M | | |
| cardona-qft-methods_FO3291 | 329 | 1.000 | d X | | |
| cardona-qft-methods_FO3292 | 329 | 1.000 | \Omega^{1}\left(\Sigma, X^{*}(T M)\right) | | |
| cardona-qft-methods_FO3293 | 329 | 1.000 | \Omega^{1}\left(\Sigma, X^{*}\left(T^{*} M\right)\right) | | |
| cardona-qft-methods_FO3294 | 329 | 1.000 | \langle | | |
| cardona-qft-methods_FO3295 | 329 | 1.000 | \rangle denotes the pairing between \Omega^{1}\left(\Sigma, X^{*}(T M)\right) | | |
| cardona-qft-methods_FO3296 | 329 | 1.000 | \mathcal{L} | | |
| cardona-qft-methods_FO3297 | 329 | 1.000 | \delta S=0 | | |
| cardona-qft-methods_FO3298 | 330 | 1.000 | { }^{6} \Phi_{\partial} | | |
| cardona-qft-methods_FO3299 | 330 | 1.000 | p: \Phi \rightarrow \Phi_{\partial} | | |
| cardona-qft-methods_FO3300 | 330 | 1.000 | C_{\Pi} | | |
| cardona-qft-methods_FO3301 | 330 | 1.000 | \Phi_{\partial} | | |
| cardona-qft-methods_FO3302 | 330 | 1.000 | L_{\Sigma^{\prime}} | | |
| cardona-qft-methods_FO3303 | 330 | 1.000 | \Sigma^{\prime}:=\partial \Sigma \times[0, \varepsilon] | | |
| cardona-qft-methods_FO3304 | 330 | 1.000 | T^{*}(P M) | | |
| cardona-qft-methods_FO3305 | 330 | 1.000 | S(X, \eta) | | |
| cardona-qft-methods_FO3306 | 330 | 0.988 | (A, \rho) | | |
| cardona-qft-methods_FO3307 | 330 | 1.000 | [,]_{A} | | |
| cardona-qft-methods_FO3308 | 330 | 1.000 | \Gamma(A) | | |
| cardona-qft-methods_FO3309 | 330 | 1.000 | \rho_{*} | | |
| cardona-qft-methods_FO3310 | 330 | 1.000 | \Gamma(A) \rightarrow \mathfrak{X}(M) | | |
| cardona-qft-methods_FO3311 | 330 | 0.516 | [,]_{T^{*} M} | | |
| cardona-qft-methods_FO3312 | 331 | 1.000 | \Pi^{\#}: T^{*} M \rightarrow T M | | |
| cardona-qft-methods_FO3313 | 331 | 1.000 | \Lambda^{\bullet} A^{*} | | |
| cardona-qft-methods_FO3314 | 331 | 1.000 | A^{*} | | |
| cardona-qft-methods_FO3315 | 331 | 1.000 | \delta_{A} | | |
| cardona-qft-methods_FO3316 | 331 | 1.000 | f \in \mathcal{C}^{\infty}(M) | | |
| cardona-qft-methods_FO3317 | 331 | 1.000 | X, Y \in \Gamma(A), \alpha \in \Gamma\left(A^{*}\right) | | |
| cardona-qft-methods_FO3318 | 331 | 0.998 | \rangle is the natural pairing between \Gamma(A) | | |
| cardona-qft-methods_FO3319 | 331 | 0.998 | \Gamma\left(A^{*}\right) | | |
| cardona-qft-methods_FO3320 | 331 | 1.000 | \varphi: A \rightarrow B | | |
| cardona-qft-methods_FO3321 | 331 | 1.000 | \gamma(A) | | |
| cardona-qft-methods_FO3322 | 331 | 1.000 | \Gamma(B) | | |
| cardona-qft-methods_FO3323 | 331 | 1.000 | T(\partial \Sigma) | | |
| cardona-qft-methods_FO3324 | 331 | 1.000 | T^{*} P M | | |
| cardona-qft-methods_FO3325 | 331 | 0.866 | M .{ }^{4} | | |
| cardona-qft-methods_FO3326 | 331 | 1.000 | G \rightrightarrows M | | |
| cardona-qft-methods_FO3327 | 331 | 1.000 | s, t, \iota, \mu | | |
| cardona-qft-methods_FO3328 | 331 | 0.578 | G_{(x, y)}:=s^{-1}(x) \cap t^{-1}(y) | | |
| cardona-qft-methods_FO3329 | 331 | 1.000 | s \circ \varepsilon=t \circ \varepsilon=i d_{M} | | |
| cardona-qft-methods_FO3330 | 331 | 1.000 | g \in G_{(x, y)} | | |
| cardona-qft-methods_FO3331 | 331 | 1.000 | h \in G_{(y, z)} | | |
| cardona-qft-methods_FO3332 | 331 | 1.000 | \mu(g, h) \in G_{(x, z)} | | |
| cardona-qft-methods_FO3333 | 331 | 0.647 | { }^{\mathrm{a}} G \times_{(s, t)} G | | |
| cardona-qft-methods_FO3334 | 332 | 1.000 | \mu\left(\varepsilon \circ s \times i d_{G}\right)=\mu\left(i d_{G} \times \varepsilon \circ t\right)=i d_{G} | | |
| cardona-qft-methods_FO3335 | 332 | 1.000 | \mu\left(i d_{G} \times i\right)=\varepsilon \circ t | | |
| cardona-qft-methods_FO3336 | 332 | 1.000 | \mu\left(i \times i d_{G}\right)=\varepsilon \circ s | | |
| cardona-qft-methods_FO3337 | 332 | 1.000 | \mu\left(\mu \times i d_{G}\right)=\mu\left(i d_{G} \times \mu\right) | | |
| cardona-qft-methods_FO3338 | 332 | 1.000 | G \times G \times \bar{G} | | |
| cardona-qft-methods_FO3339 | 332 | 1.000 | \bar{G} | | |
| cardona-qft-methods_FO3340 | 332 | 0.984 | \underline{C_{\Pi}} | | |
| cardona-qft-methods_FO3341 | 332 | 1.000 | \mathcal{A}=T^{*} M | | |
| cardona-qft-methods_FO3342 | 332 | 0.999 | { }^{\text {Ext }} | | |
| cardona-qft-methods_FO3343 | 333 | 0.905 | { }^{E x t} | | |
| cardona-qft-methods_FO3344 | 333 | 1.000 | L: \mathcal{M} \nrightarrow \mathcal{N} | | |
| cardona-qft-methods_FO3345 | 333 | 1.000 | \mathcal{N} | | |
| cardona-qft-methods_FO3346 | 333 | 0.755 | \overline{\mathcal{M}} \times \mathcal{N} | | |
| cardona-qft-methods_FO3347 | 333 | 0.755 | { }^{\text {c }} | | |
| cardona-qft-methods_FO3348 | 333 | 0.755 | \left(\text { Sym }^{\text {Ext }}\right)^{\text {op }} \rightarrow | | |
| cardona-qft-methods_FO3349 | 333 | 0.755 | ^{\text {Ext }} | | |
| cardona-qft-methods_FO3350 | 333 | 1.000 | f: A \nrightarrow B | | |
| cardona-qft-methods_FO3351 | 333 | 1.000 | f^{\dagger}:=\{(b, a) \in B \times A \mid(a, b) \in f\} | | |
| cardona-qft-methods_FO3352 | 333 | 0.863 | (\mathcal{G}, L, I) | | |
| cardona-qft-methods_FO3353 | 333 | 1.000 | \mathcal{G}^{3} | | |
| cardona-qft-methods_FO3354 | 333 | 1.000 | 1 L | | |
| cardona-qft-methods_FO3355 | 333 | 1.000 | (x, y, z) \in L | | |
| cardona-qft-methods_FO3356 | 333 | 1.000 | (y, z, x) \in L | | |
| cardona-qft-methods_FO3357 | 333 | 0.995 | 2 I | | |
| cardona-qft-methods_FO3358 | 333 | 0.995 | I^{2}=I d | | |
| cardona-qft-methods_FO3359 | 333 | 1.000 | \mathcal{G} \times \mathcal{G} \nrightarrow \overline{\mathcal{G}} | | |
| cardona-qft-methods_FO3360 | 333 | 1.000 | L_{\text {rel }} | | |
| cardona-qft-methods_FO3361 | 333 | 1.000 | \mathcal{G} \times \mathcal{G}, I | | |
| cardona-qft-methods_FO3362 | 333 | 0.996 | \overline{\mathcal{G}} \nrightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3363 | 333 | 0.996 | I_{\text {rel }} | | |
| cardona-qft-methods_FO3364 | 333 | 0.995 | \overline{L_{r e l}} | | |
| cardona-qft-methods_FO3365 | 333 | 0.995 | \overline{I_{r e l}} | | |
| cardona-qft-methods_FO3366 | 333 | 1.000 | \omega^{\#}: T^{*} M \rightarrow T M | | |
| cardona-qft-methods_FO3367 | 334 | 0.999 | I d: \mathcal{G} \rightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3368 | 334 | 0.999 | I d_{\text {rel }} | | |
| cardona-qft-methods_FO3369 | 334 | 1.000 | \mathcal{G} \nrightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3370 | 334 | 1.000 | \overline{I d_{r e l}}: \overline{\mathcal{G}} \nrightarrow \overline{\mathcal{G}} | | |
| cardona-qft-methods_FO3371 | 334 | 0.927 | 3 I_{\text {rel }} \circ L_{\text {rel }}=\bar{L}_{\text {rel }} \circ \bar{T}_{\text {rel }} \circ\left(\overline{I_{\text {rel }}} \circ \overline{I_{\text {rel }}}\right): \mathcal{G} \times \mathcal{G} \nrightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3372 | 334 | 0.997 | \overline{I_{\text {rel }}} \circ L_{3}=\overline{L_{3}} \circ \overline{T_{\text {rel }}} \circ\left(\overline{I_{\text {rel }}} \times \overline{I_{\text {rel }}}\right) | | |
| cardona-qft-methods_FO3373 | 334 | 1.000 | 4 L_{3} \circ\left(L_{3} \times I d\right)=L_{3} \circ\left(I d \times L_{3}\right): \mathcal{G}^{3} \nrightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3374 | 334 | 0.999 | \left(I d \times L_{3}\right) | | |
| cardona-qft-methods_FO3375 | 334 | 0.999 | \left(L_{3} \times I d\right) | | |
| cardona-qft-methods_FO3376 | 334 | 1.000 | * \nrightarrow \mathcal{G} \times \mathcal{G} | | |
| cardona-qft-methods_FO3377 | 334 | 1.000 | L_{I} | | |
| cardona-qft-methods_FO3378 | 334 | 1.000 | 5 L_{3} \circ L_{I} | | |
| cardona-qft-methods_FO3379 | 334 | 1.000 | L_{1}:=L_{3} \circ L_{I}: * \nrightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3380 | 334 | 1.000 | L_{1} | | |
| cardona-qft-methods_FO3381 | 335 | 1.000 | 6 L_{3} \circ\left(L_{1} \times I d\right) | | |
| cardona-qft-methods_FO3382 | 335 | 1.000 | \overline{\mathcal{G}} \times \mathcal{G} | | |
| cardona-qft-methods_FO3383 | 335 | 1.000 | L_{2} | | |
| cardona-qft-methods_FO3384 | 335 | 1.000 | * \nrightarrow \mathcal{G} | | |
| cardona-qft-methods_FO3385 | 335 | 1.000 | \mathcal{G}_{\text {rel }} | | |
| cardona-qft-methods_FO3386 | 335 | 0.989 | 7 L_{2} \circ \mathcal{G}_{\text {rel }} | | |
| cardona-qft-methods_FO3387 | 335 | 1.000 | C:=L_{2} \circ \mathcal{G}_{\text {rel }} | | |
| cardona-qft-methods_FO3388 | 335 | 0.999 | \underline{L_{1}}=L_{1} / L_{2} | | |
| cardona-qft-methods_FO3389 | 335 | 1.000 | \underline{L_{1}} | | |
| cardona-qft-methods_FO3390 | 336 | 1.000 | 9 S:=\left\{(c,[l]) \in C \times M: \exists l \in[l], g \in \mathcal{G} \mid(l, c, g) \in L_{3}\right\} | | |
| cardona-qft-methods_FO3391 | 336 | 1.000 | \mathcal{G} \times M | | |
| cardona-qft-methods_FO3392 | 336 | 0.655 | \mathcal{G}, L, I | | |
| cardona-qft-methods_FO3393 | 336 | 1.000 | G:=C / L_{2} | | |
| cardona-qft-methods_FO3394 | 336 | 1.000 | s:=S / L_{2}, t:=T / L_{2}, \mu:= | | |
| cardona-qft-methods_FO3395 | 336 | 0.898 | L_{\text {rel }} / L_{2}, \iota=I, \varepsilon=L_{1} / L_{2} | | |
| cardona-qft-methods_FO3396 | 336 | 0.998 | \left(G, L_{G}, I_{G}\right) | | |
| cardona-qft-methods_FO3397 | 336 | 0.998 | \left(H, L_{H}, I_{H}\right) | | |
| cardona-qft-methods_FO3398 | 336 | 1.000 | G \times \bar{H} | | |
| cardona-qft-methods_FO3399 | 336 | 1.000 | F \circ I_{G}=I_{H} \circ F | | |
| cardona-qft-methods_FO3400 | 336 | 1.000 | F^{3}\left(L_{G}\right)=L_{H} | | |
| cardona-qft-methods_FO3401 | 336 | 1.000 | F: G \rightarrow | | |
| cardona-qft-methods_FO3402 | 336 | 0.998 | F^{\dagger} | | |
| cardona-qft-methods_FO3403 | 336 | 0.965 | \mathcal{C}^{k} | | |
| cardona-qft-methods_FO3404 | 337 | 0.909 | (G, \omega) | | |
| cardona-qft-methods_FO3405 | 337 | 0.998 | G_{(1)}=G, G_{(2)} | | |
| cardona-qft-methods_FO3406 | 337 | 0.998 | G \times_{(s, t)} G, G_{(3)}=G \times_{(s, t)} | | |
| cardona-qft-methods_FO3407 | 337 | 0.615 | \left(G \times_{(s, t)} G\right) | | |
| cardona-qft-methods_FO3408 | 337 | 0.998 | G_{(n)} | | |
| cardona-qft-methods_FO3409 | 337 | 0.998 | G^{n} | | |
| cardona-qft-methods_FO3410 | 338 | 1.000 | P_{n}: \underline{G_{(n)}} \rightarrow G^{n} | | |
| cardona-qft-methods_FO3411 | 338 | 1.000 | G_{(i)} | | |
| cardona-qft-methods_FO3412 | 338 | 1.000 | G_{(j)}, \forall i, j \geq 1 | | |
| cardona-qft-methods_FO3413 | 338 | 1.000 | P_{i} \circ P_{j}^{\dagger} | | |
| cardona-qft-methods_FO3414 | 338 | 0.966 | \sim | | |
| cardona-qft-methods_FO3415 | 339 | 1.000 | (\overline{X, \eta})=\left\{(X, \eta) \mid X \equiv X_{0}, \eta \in \operatorname{ker} \Pi^{\#}\right\} | | |
| cardona-qft-methods_FO3416 | 339 | 1.000 | N\left(\Gamma_{0}\left(T^{*} P M\right)\right) | | |
| cardona-qft-methods_FO3417 | 339 | 1.000 | \overline{L_{1}} \cap N\left(\Gamma_{0}\left(T^{*} P M\right)\right) | | |
| cardona-qft-methods_FO3418 | 339 | 1.000 | L_{1} \cap N\left(\Gamma_{0}\left(T^{*} P M\right)\right), L_{2} \cap | | |
| cardona-qft-methods_FO3419 | 339 | 1.000 | N\left(\Gamma_{0}\left(T^{*} P M\right)\right)^{2} | | |
| cardona-qft-methods_FO3420 | 339 | 1.000 | L_{3} \cap N\left(\Gamma_{0}\left(T^{*} P M\right)\right)^{3} | | |
| cardona-qft-methods_FO3421 | 339 | 0.971 | \rangle and an asso- | | |
| cardona-qft-methods_FO3422 | 339 | 1.000 | { }^{-} | | |
| cardona-qft-methods_FO3423 | 339 | 1.000 | \left\{e_{i}\right\} | | |
| cardona-qft-methods_FO3424 | 340 | 0.998 | \left(H, m,\langle,\rangle_{H}\right) | | |
| cardona-qft-methods_FO3425 | 342 | 1.000 | L M | | |
| cardona-qft-methods_FO3426 | 342 | 1.000 | -n | | |
| cardona-qft-methods_FO3427 | 343 | 1.000 | [* / G] | | |
| cardona-qft-methods_FO3428 | 343 | 1.000 | H^{*}(L B G) | | |
| cardona-qft-methods_FO3429 | 343 | 1.000 | H_{p}(M) \cong\left(H^{p}(M)\right)^{*} | | |
| cardona-qft-methods_FO3430 | 343 | 1.000 | H_{*+n}(M) | | |
| cardona-qft-methods_FO3431 | 344 | 1.000 | \sigma \in H_{p}(M), \tau \in H_{q}(M) | | |
| cardona-qft-methods_FO3432 | 344 | 0.958 | { }^{\mathrm{a}} P^{p} \subseteq M | | |
| cardona-qft-methods_FO3433 | 344 | 0.958 | Q^{q} \subseteq M | | |
| cardona-qft-methods_FO3434 | 344 | 1.000 | P \cap Q | | |
| cardona-qft-methods_FO3435 | 344 | 0.951 | \Delta: M \rightarrow M \times M | | |
| cardona-qft-methods_FO3436 | 344 | 1.000 | \nu_{\Delta} | | |
| cardona-qft-methods_FO3437 | 344 | 1.000 | (M \times M) / \nu_{\Delta}^{c} | | |
| cardona-qft-methods_FO3438 | 344 | 1.000 | M^{T M} | | |
| cardona-qft-methods_FO3439 | 344 | 1.000 | e: P \rightarrow Q | | |
| cardona-qft-methods_FO3440 | 344 | 1.000 | Q \rightarrow P^{\nu(e)} | | |
| cardona-qft-methods_FO3441 | 344 | 1.000 | \nu(e) \rightarrow P | | |
| cardona-qft-methods_FO3442 | 344 | 1.000 | e_{!}: H_{*}(Q) \rightarrow H_{*-\operatorname{dim} \nu(e)}(P) | | |
| cardona-qft-methods_FO3443 | 344 | 1.000 | \sigma \in H_{p}(M) | | |
| cardona-qft-methods_FO3444 | 345 | 1.000 | \operatorname{Map}(8, M) | | |
| cardona-qft-methods_FO3445 | 345 | 0.991 | e v: L M \rightarrow M | | |
| cardona-qft-methods_FO3446 | 345 | 0.570 | M a p(8, M) \rightarrow L M \times L M | | |
| cardona-qft-methods_FO3447 | 345 | 1.000 | M \rightarrow M \times M | | |
| cardona-qft-methods_FO3448 | 345 | 0.927 | \tau_{\Delta}: L M \times L M \rightarrow \operatorname{Map}(8, M)^{e v^{*}(T M)} | | |
| cardona-qft-methods_FO3449 | 345 | 0.745 | \operatorname{Map}(8, M) \rightarrow L M | | |
| cardona-qft-methods_FO3450 | 345 | 1.000 | \Omega M \times \Omega M \rightarrow \Omega M | | |
| cardona-qft-methods_FO3451 | 346 | 1.000 | L M^{-T M} | | |
| cardona-qft-methods_FO3452 | 346 | 1.000 | -T M \rightarrow M | | |
| cardona-qft-methods_FO3453 | 346 | 1.000 | M^{-T M} \simeq F\left(M_{+}, S\right) | | |
| cardona-qft-methods_FO3454 | 346 | 1.000 | M^{-T M} | | |
| cardona-qft-methods_FO3455 | 346 | 0.999 | M_{+}{ }^{\mathrm{b}} | | |
| cardona-qft-methods_FO3456 | 346 | 0.999 | H_{*}\left(M^{-T M}\right) \cong | | |
| cardona-qft-methods_FO3457 | 346 | 1.000 | H_{*}\left(F\left(M_{+}, S\right)\right) \cong H^{-*}(M) | | |
| cardona-qft-methods_FO3458 | 346 | 1.000 | e: M \hookrightarrow \mathbb{R}^{k} | | |
| cardona-qft-methods_FO3459 | 346 | 1.000 | \nu(e) \rightarrow M | | |
| cardona-qft-methods_FO3460 | 346 | 0.999 | M^{\nu(e)} | | |
| cardona-qft-methods_FO3461 | 346 | 0.894 | M \times M \rightarrow M^{T M} | | |
| cardona-qft-methods_FO3462 | 346 | 0.894 | -2 T M | | |
| cardona-qft-methods_FO3463 | 346 | 0.997 | \operatorname{Map}(8, M) \rightarrow | | |
| cardona-qft-methods_FO3464 | 346 | 1.000 | e v^{*}(-T M) | | |
| cardona-qft-methods_FO3465 | 346 | 0.481 | M a p(8, M)^{e v^{*}}(-T M) \rightarrow L M^{e v^{*}(-T M)} | | |
| cardona-qft-methods_FO3466 | 346 | 0.998 | e v^{*}(-2 T M) | | |
| cardona-qft-methods_FO3467 | 346 | 0.999 | X_{+} | | |
| cardona-qft-methods_FO3468 | 346 | 1.000 | F\left(X_{+}, Y\right) | | |
| cardona-qft-methods_FO3469 | 347 | 0.716 | 1.2\left(^{7}\right) | | |
| cardona-qft-methods_FO3470 | 347 | 0.811 | L M^{e v^{*}(-T M)} | | |
| cardona-qft-methods_FO3471 | 347 | 0.999 | 1.3\left({ }^{\mathbf{7}}\right) | | |
| cardona-qft-methods_FO3472 | 348 | 0.979 | \bar{U}, G, U | | |
| cardona-qft-methods_FO3473 | 348 | 0.979 | \bar{U} | | |
| cardona-qft-methods_FO3474 | 348 | 1.000 | \bar{U} / G | | |
| cardona-qft-methods_FO3475 | 348 | 0.910 | \bar{U}_{\alpha}, G_{\alpha}, U_{\alpha} | | |
| cardona-qft-methods_FO3476 | 348 | 1.000 | [M / G] | | |
| cardona-qft-methods_FO3477 | 348 | 0.936 | x \in X | | |
| cardona-qft-methods_FO3478 | 348 | 0.936 | \bar{x} \in \bar{U} | | |
| cardona-qft-methods_FO3479 | 348 | 1.000 | G_{x} | | |
| cardona-qft-methods_FO3480 | 348 | 1.000 | \mathbb{C}^{2}-\{0\} | | |
| cardona-qft-methods_FO3481 | 348 | 1.000 | \lambda\left(z_{1}, z_{2}\right)= | | |
| cardona-qft-methods_FO3482 | 348 | 0.999 | \left(\lambda^{2} z, \lambda z\right) | | |
| cardona-qft-methods_FO3483 | 348 | 0.999 | \mathcal{X} | | |
| cardona-qft-methods_FO3484 | 348 | 0.999 | B \mathcal{X} | | |
| cardona-qft-methods_FO3485 | 348 | 1.000 | \mathcal{X}=[M / G] | | |
| cardona-qft-methods_FO3486 | 348 | 1.000 | M, B \mathcal{X} | | |
| cardona-qft-methods_FO3487 | 349 | 1.000 | E G \times_{G} M | | |
| cardona-qft-methods_FO3488 | 349 | 1.000 | E G \rightarrow B G | | |
| cardona-qft-methods_FO3489 | 349 | 0.993 | |\mathcal{X}| | | |
| cardona-qft-methods_FO3490 | 349 | 0.993 | B \mathcal{X} \rightarrow|\mathcal{X}| | | |
| cardona-qft-methods_FO3491 | 349 | 1.000 | \left[P_{G} M / G\right] | | |
| cardona-qft-methods_FO3492 | 349 | 1.000 | M \times_{G} E G | | |
| cardona-qft-methods_FO3493 | 349 | 1.000 | [X / G] | | |
| cardona-qft-methods_FO3494 | 349 | 1.000 | X \times G | | |
| cardona-qft-methods_FO3495 | 349 | 1.000 | s(x, g)=x | | |
| cardona-qft-methods_FO3496 | 349 | 1.000 | t(x, g)=x g | | |
| cardona-qft-methods_FO3497 | 349 | 1.000 | [\mathbf{R} / \mathbf{Z}] | | |
| cardona-qft-methods_FO3498 | 349 | 1.000 | \left[P_{G} X / G\right] | | |
| cardona-qft-methods_FO3499 | 350 | 1.000 | e_{t}: P_{g} M \rightarrow M | | |
| cardona-qft-methods_FO3500 | 350 | 1.000 | t: e_{t}(f):=f(t) | | |
| cardona-qft-methods_FO3501 | 350 | 1.000 | e_{0} \circ \pi_{1} | | |
| cardona-qft-methods_FO3502 | 350 | 1.000 | \Delta_{g} | | |
| cardona-qft-methods_FO3503 | 350 | 0.820 | P_{g} M \times P_{h} M \rightarrow P_{g} M:{ }_{1} \times_{0} P_{h} M^{\pi_{1}^{*}} e_{0}^{*} N_{g} | | |
| cardona-qft-methods_FO3504 | 350 | 0.806 | P_{g} M^{-e_{0}^{*} T M} \wedge P_{h} M^{-e_{0}^{*} T M} \rightarrow P_{g} M:{ }_{1} \times_{0} P_{h} M^{-\pi_{1}^{*}} e_{0}^{*} T M | | |
| cardona-qft-methods_FO3505 | 350 | 0.991 | P_{g} M:{ }_{1} \times_{0} P_{h} M | | |
| cardona-qft-methods_FO3506 | 350 | 0.991 | P_{g} M:{ }_{1} \times_{0} P_{h} M \rightarrow P_{g h} M | | |
| cardona-qft-methods_FO3507 | 350 | 0.926 | P_{g} M:{ }_{1} \times_{0} P_{h} M^{-\pi_{1}^{*}} e_{0}^{*} T M \rightarrow P_{g h} M^{-e_{0}^{*} T M} | | |
| cardona-qft-methods_FO3508 | 350 | 1.000 | \mu_{g, h}: P_{g} M^{-e_{0}^{*} T M} \wedge P_{h} M^{-e_{0}^{*} T M} \rightarrow P_{g h} M^{-e_{0}^{*} T M} | | |
| cardona-qft-methods_FO3509 | 350 | 1.000 | \mu_{g, h} | | |
| cardona-qft-methods_FO3510 | 350 | 0.546 | 3.1\left({ }^{\mathbf{1 4}}\right) . P_{G} M^{-T M} | | |
| cardona-qft-methods_FO3511 | 350 | 1.000 | H_{*}\left(P_{G} M^{-T M} ; \mathbb{Z}\right) | | |
| cardona-qft-methods_FO3512 | 351 | 1.000 | C^{*}(M ; \mathbb{Q}) \# G | | |
| cardona-qft-methods_FO3513 | 351 | 1.000 | C^{*}(M) \# G | | |
| cardona-qft-methods_FO3514 | 351 | 1.000 | C^{*}(X) \# G | | |
| cardona-qft-methods_FO3515 | 351 | 1.000 | \left(C^{*}(X) \# G\right)^{e} | | |
| cardona-qft-methods_FO3516 | 351 | 1.000 | g \cdot(x \otimes h) \mapsto g(x) \otimes g h g^{-1} | | |
| cardona-qft-methods_FO3517 | 351 | 0.951 | H H^{*}\left(C^{*}(X) \# G, C^{*}(X) \# G\right) \cong \operatorname{Ext}_{\mathbb{Z} G}^{*}\left(\mathbb{Z}, \mathcal{R} \mathcal{H} o m_{C^{*}(X)^{e}}\left(C^{*}(X), C^{*}(X) \# G\right)\right) | | |
| cardona-qft-methods_FO3518 | 351 | 0.984 | P_{G} X, \mathrm{in}^{3} | | |
| cardona-qft-methods_FO3519 | 351 | 1.000 | P_{G} M | | |
| cardona-qft-methods_FO3520 | 352 | 1.000 | E G | | |
| cardona-qft-methods_FO3521 | 352 | 1.000 | E G_{1} \subset \cdots \subset E G_{n} \subset E G_{n+1} \subset \cdots E G | | |
| cardona-qft-methods_FO3522 | 352 | 1.000 | E G \rightarrow | | |
| cardona-qft-methods_FO3523 | 352 | 1.000 | B G | | |
| cardona-qft-methods_FO3524 | 352 | 1.000 | (f, \lambda) \in P_{G} M \times_{G} E G_{n} | | |
| cardona-qft-methods_FO3525 | 352 | 1.000 | e_{t} | | |
| cardona-qft-methods_FO3526 | 352 | 1.000 | M_{n}=M \times_{G} E G_{n} | | |
| cardona-qft-methods_FO3527 | 352 | 1.000 | M_{n} | | |
| cardona-qft-methods_FO3528 | 352 | 1.000 | e_{0} | | |
| cardona-qft-methods_FO3529 | 352 | 1.000 | E G_{n} \subset E G_{n+1} \subset \cdots E G | | |
| cardona-qft-methods_FO3530 | 352 | 1.000 | \mathbb{L}\left(M \times_{G} E G\right)^{-T\left(M \times_{G} E G\right)} | | |
| cardona-qft-methods_FO3531 | 353 | 0.548 | 3.5\left(^{\mathbf{3}}\right) | | |
| cardona-qft-methods_FO3532 | 353 | 1.000 | M=* | | |
| cardona-qft-methods_FO3533 | 353 | 1.000 | L B G^{-T B G} | | |
| cardona-qft-methods_FO3534 | 353 | 0.919 | \mathrm{L}[* / G] | | |
| cardona-qft-methods_FO3535 | 353 | 0.919 | \left[G^{a d} / G\right] | | |
| cardona-qft-methods_FO3536 | 353 | 1.000 | C(g) | | |
| cardona-qft-methods_FO3537 | 353 | 1.000 | H_{*}\left(P_{G} M^{-T M} ; \mathbb{Q}\right)^{G} \cong \mathbb{Q} G | | |
| cardona-qft-methods_FO3538 | 353 | 1.000 | B G_{n}:=E G_{n} / G | | |
| cardona-qft-methods_FO3539 | 353 | 1.000 | \left(G^{a d} \times_{G} E G_{n}\right)^{-T B G_{n}} | | |
| cardona-qft-methods_FO3540 | 353 | 0.999 | G^{a d} \times_{G} E G_{n} | | |
| cardona-qft-methods_FO3541 | 353 | 1.000 | \bigsqcup_{(g)} E G_{n} / C(g) | | |
| cardona-qft-methods_FO3542 | 353 | 1.000 | T\left(G^{a d} \times_{G} E G_{n}\right) | | |
| cardona-qft-methods_FO3543 | 353 | 1.000 | \bigsqcup_{(g)} T\left(E G_{n} / C(g)\right) | | |
| cardona-qft-methods_FO3544 | 353 | 1.000 | E H | | |
| cardona-qft-methods_FO3545 | 353 | 1.000 | H \subseteq G | | |
| cardona-qft-methods_FO3546 | 353 | 1.000 | E G_{1} \subset \cdots \subset E G_{n} \subset E G_{n+1} \subset \cdots | | |
| cardona-qft-methods_FO3547 | 353 | 1.000 | E C(g) | | |
| cardona-qft-methods_FO3548 | 353 | 1.000 | \bigoplus_{(g)} H_{*}\left(\left(B C(g)_{n}\right)^{-T B C(g)_{n}}\right) | | |
| cardona-qft-methods_FO3549 | 353 | 1.000 | \bigoplus_{(g)} H^{*}\left(B C(g)_{n}\right) | | |
| cardona-qft-methods_FO3550 | 353 | 1.000 | \bigoplus_{(g)} H^{*}(B C(g)) | | |
| cardona-qft-methods_FO3551 | 354 | 1.000 | k_{n}=\operatorname{dim}\left(E G_{n}\right) | | |
| cardona-qft-methods_FO3552 | 354 | 0.979 | H_{*}^{\text {pro }}\left(\mathbb{L} B G^{-T B G}\right) | | |
| cardona-qft-methods_FO3553 | 354 | 1.000 | H^{*}(B C(g)) | | |
| cardona-qft-methods_FO3554 | 354 | 1.000 | H^{*}(B C(h)) | | |
| cardona-qft-methods_FO3555 | 354 | 1.000 | H^{*}(B(C(g) \cap | | |
| cardona-qft-methods_FO3556 | 354 | 0.835 | C(h))) | | |
| cardona-qft-methods_FO3557 | 354 | 0.835 | H^{*}(B C(g h)) | | |
| cardona-qft-methods_FO3558 | 354 | 1.000 | H^{*}(B G) \otimes \mathbb{Z} G | | |
| cardona-qft-methods_FO3559 | 354 | 1.000 | L B G^{-a d} | | |
| cardona-qft-methods_FO3560 | 354 | 1.000 | L B G | | |
| cardona-qft-methods_FO3561 | 354 | 1.000 | L B G \cong E G \times_{G} G | | |
| cardona-qft-methods_FO3562 | 354 | 1.000 | \mu: G \times G \rightarrow G | | |
| cardona-qft-methods_FO3563 | 354 | 1.000 | m_{!}: G_{+} \rightarrow G \wedge G_{+} | | |
| cardona-qft-methods_FO3564 | 354 | 1.000 | E G \times_{G} G \rightarrow E G \times_{G}(G \times G) | | |
| cardona-qft-methods_FO3565 | 354 | 1.000 | E G \times_{G}(G \times G) \rightarrow\left(E G \times_{G} G\right) \times\left(E G \times_{G} G\right) | | |
| cardona-qft-methods_FO3566 | 354 | 1.000 | E G \times_{G} G \rightarrow | | |
| cardona-qft-methods_FO3567 | 355 | 0.887 | \left(E G \times_{G} G\right) \times\left(E G \times_{G} G\right) | | |
| cardona-qft-methods_FO3568 | 355 | 0.989 | \operatorname{Map}(\Theta, B G) \rightarrow L B G | | |
| cardona-qft-methods_FO3569 | 355 | 0.989 | \Omega B G | | |
| cardona-qft-methods_FO3570 | 355 | 0.927 | H^{*}(\operatorname{Map}(\Theta, B G)) \rightarrow | | |
| cardona-qft-methods_FO3571 | 355 | 0.751 | H^{*}(\operatorname{Map}(\Theta, B G)) \rightarrow H^{*}(L B G) | | |
| cardona-qft-methods_FO3572 | 355 | 0.915 | H^{*}(L B G) \otimes H^{*}(L B G) \rightarrow H^{*}(\operatorname{Map}(\Theta, B G) | | |
| cardona-qft-methods_FO3573 | 357 | 1.000 | \mathbb{P}_{k}^{n-1} | | |
| cardona-qft-methods_FO3574 | 358 | 0.999 | { }^{1,4} | | |
| cardona-qft-methods_FO3575 | 358 | 1.000 | \mathcal{V}_{k} | | |
| cardona-qft-methods_FO3576 | 358 | 1.000 | K_{0}\left(\mathcal{V}_{k}\right) | | |
| cardona-qft-methods_FO3577 | 358 | 1.000 | Y \subset X | | |
| cardona-qft-methods_FO3578 | 358 | 1.000 | X=Y | | |
| cardona-qft-methods_FO3579 | 358 | 1.000 | \chi: \mathcal{V}_{k} \rightarrow R | | |
| cardona-qft-methods_FO3580 | 358 | 1.000 | \chi(X)=\chi(Y) | | |
| cardona-qft-methods_FO3581 | 358 | 1.000 | \chi(X \backslash Y)=\chi(X)-\chi(Y) | | |
| cardona-qft-methods_FO3582 | 358 | 1.000 | \chi(X \times Y)=\chi(X) \chi(Y) | | |
| cardona-qft-methods_FO3583 | 358 | 1.000 | \mathbb{L}=\left[\mathbb{A}_{k}^{1}\right] | | |
| cardona-qft-methods_FO3584 | 358 | 1.000 | \mathbb{A}_{k}^{1} | | |
| cardona-qft-methods_FO3585 | 358 | 1.000 | \mathbb{A}_{k}^{n} | | |
| cardona-qft-methods_FO3586 | 359 | 1.000 | k^{\times} | | |
| cardona-qft-methods_FO3587 | 359 | 1.000 | X \backslash(X \cap Y)=(X \cup Y) \backslash Y | | |
| cardona-qft-methods_FO3588 | 359 | 1.000 | \mathbb{P}_{k}^{n+1} \backslash \mathbb{A}_{k}^{n+1} \simeq \mathbb{P}_{k}^{n} | | |
| cardona-qft-methods_FO3589 | 359 | 0.992 | t_{1}, t_{2}, \ldots, t_{n} | | |
| cardona-qft-methods_FO3590 | 359 | 0.992 | Z\left[t_{1}, t_{2}, \ldots, t_{n}\right] | | |
| cardona-qft-methods_FO3591 | 360 | 1.000 | E(T) | | |
| cardona-qft-methods_FO3592 | 360 | 1.000 | v-1 | | |
| cardona-qft-methods_FO3593 | 360 | 1.000 | \Psi_{\Gamma}(t) | | |
| cardona-qft-methods_FO3594 | 360 | 1.000 | n-v+1 | | |
| cardona-qft-methods_FO3595 | 360 | 1.000 | X_{\Gamma} | | |
| cardona-qft-methods_FO3596 | 360 | 1.000 | \Gamma^{\vee} | | |
| cardona-qft-methods_FO3597 | 360 | 1.000 | \mathbb{S}^{2} | | |
| cardona-qft-methods_FO3598 | 360 | 0.997 | \Psi_{\Gamma^{\vee}}(t) | | |
| cardona-qft-methods_FO3599 | 360 | 0.820 | { }^{1,2} | | |
| cardona-qft-methods_FO3600 | 360 | 0.820 | X_{\Gamma \vee} | | |
| cardona-qft-methods_FO3601 | 361 | 1.000 | \mathbb{P}_{k}^{n-1} \times \mathbb{P}_{k}^{n-1} | | |
| cardona-qft-methods_FO3602 | 361 | 1.000 | \mathcal{G}(\mathcal{C}) | | |
| cardona-qft-methods_FO3603 | 361 | 1.000 | \pi_{1} | | |
| cardona-qft-methods_FO3604 | 361 | 1.000 | \pi_{2} | | |
| cardona-qft-methods_FO3605 | 361 | 0.902 | \left(t_{1}: t_{2}: \cdots: t_{2 n}\right) | | |
| cardona-qft-methods_FO3606 | 361 | 1.000 | \pi_{i} | | |
| cardona-qft-methods_FO3607 | 361 | 1.000 | \pi_{2}: \mathcal{G}(\mathcal{C}) \rightarrow \mathbb{P}_{k}^{n-1} | | |
| cardona-qft-methods_FO3608 | 362 | 1.000 | \mathcal{G}(C) | | |
| cardona-qft-methods_FO3609 | 362 | 0.998 | X_{\Gamma^{\vee}} | | |
| cardona-qft-methods_FO3610 | 362 | 0.998 | \Sigma_{n} | | |
| cardona-qft-methods_FO3611 | 362 | 1.000 | \left(k^{\times}\right)^{n-1} | | |
| cardona-qft-methods_FO3612 | 362 | 1.000 | \mathbb{T}^{n-1} | | |
| cardona-qft-methods_FO3613 | 362 | 1.000 | X_{\Gamma^{\vee}}=\Sigma_{n}=\mathbb{P}_{k}^{n-1} \backslash\left(k^{\times}\right)^{n-1} | | |
| cardona-qft-methods_FO3614 | 363 | 0.996 | t_{1}, t_{2}, \ldots, t_{n-1} | | |
| cardona-qft-methods_FO3615 | 363 | 1.000 | t_{n} | | |
| cardona-qft-methods_FO3616 | 363 | 1.000 | \mathbb{P}_{k}^{n-2} | | |
| cardona-qft-methods_FO3617 | 363 | 0.997 | (n-1) | | |
| cardona-qft-methods_FO3618 | 363 | 1.000 | t_{i} | | |
| cardona-qft-methods_FO3619 | 363 | 1.000 | \hat{t_{i}} | | |
| cardona-qft-methods_FO3620 | 363 | 1.000 | X_{\Gamma} \backslash \Sigma_{n} | | |
| cardona-qft-methods_FO3621 | 363 | 0.930 | X_{\Gamma^{\vee}} \backslash \Sigma_{n} | | |
| cardona-qft-methods_FO3622 | 363 | 1.000 | X_{\Gamma} \backslash \Sigma | | |
| cardona-qft-methods_FO3623 | 363 | 1.000 | \mathcal{L} \cap \Sigma_{n} | | |
| cardona-qft-methods_FO3624 | 363 | 1.000 | C=g(\mathbb{T}) | | |
| cardona-qft-methods_FO3625 | 364 | 1.000 | g(\mathbb{T})=\left[\mathbb{P}^{n}\right]=\frac{(\mathbb{T}-1)^{n}-1}{\mathbb{T}} | | |
| cardona-qft-methods_FO3626 | 364 | 1.000 | \left[\Sigma_{n}\right]=\frac{(\mathbb{T}+1)^{n}-1-\mathbb{T}^{n}}{\mathbb{T}}=g(\mathbb{T}) | | |
| cardona-qft-methods_FO3627 | 364 | 1.000 | \mathcal{S}_{n} | | |
| cardona-qft-methods_FO3628 | 364 | 1.000 | \Sigma_{n-1} | | |
| cardona-qft-methods_FO3629 | 365 | 0.995 | \left[X_{\Gamma^{\vee}}\right] | | |
| cardona-qft-methods_FO3630 | 365 | 0.989 | \left[X_{\Gamma^{\vee}} \backslash \Sigma\right] | | |
| cardona-qft-methods_FO3631 | 365 | 0.989 | \left[\mathcal{S}_{n}\right] | | |
| cardona-qft-methods_FO3632 | 366 | 1.000 | p(t) | | |
| cardona-qft-methods_FO3633 | 366 | 1.000 | q(t) | | |
| cardona-qft-methods_FO3634 | 366 | 1.000 | t_{i}=x | | |
| cardona-qft-methods_FO3635 | 366 | 1.000 | t_{j}, j \neq i | | |
| cardona-qft-methods_FO3636 | 366 | 1.000 | \Psi_{\Gamma}(x) | | |
| cardona-qft-methods_FO3637 | 366 | 1.000 | p(x) | | |
| cardona-qft-methods_FO3638 | 366 | 1.000 | q(x) | | |
| cardona-qft-methods_FO3639 | 366 | 1.000 | t_{j} | | |
| cardona-qft-methods_FO3640 | 367 | 1.000 | P \cap Q=\emptyset, P \cup Q | | |
| cardona-qft-methods_FO3641 | 367 | 1.000 | \Psi_{\Gamma} | | |
| cardona-qft-methods_FO3642 | 368 | 1.000 | \tilde{m} g | | |
| cardona-qft-methods_FO3643 | 368 | 0.960 | \mathbb{I} \pi | | |
| cardona-qft-methods_FO3644 | 368 | 1.000 | g \mapsto\langle\xi, \pi(g) \eta\rangle | | |
| cardona-qft-methods_FO3645 | 368 | 1.000 | M=G / H | | |
| cardona-qft-methods_FO3646 | 368 | 1.000 | \mathcal{E}(\tilde{m} g) | | |
| cardona-qft-methods_FO3647 | 368 | 1.000 | \mathbb{C}[G] | | |
| cardona-qft-methods_FO3648 | 368 | 1.000 | g \otimes h \mapsto g h | | |
| cardona-qft-methods_FO3649 | 368 | 1.000 | g \mapsto g^{-1} | | |
| cardona-qft-methods_FO3650 | 368 | 1.000 | \bar{g}=g | | |
| cardona-qft-methods_FO3651 | 368 | 1.000 | \mathcal{E}=\mathcal{E}(\tilde{m} g) | | |
| cardona-qft-methods_FO3652 | 369 | 1.000 | \mathcal{T}(\tilde{m} g)=\left(\bigoplus_{n \in \mathbb{N}} \tilde{m} g^{\otimes n}\right) \otimes \mathbb{C} | | |
| cardona-qft-methods_FO3653 | 369 | 1.000 | \left(X_{1} \cdots X_{n}\right)^{\dagger}=(-1)^{n} X_{n} \cdots X_{1} | | |
| cardona-qft-methods_FO3654 | 369 | 1.000 | \overline{X_{1} \cdots X_{n}}=X_{1} \cdots X_{n} | | |
| cardona-qft-methods_FO3655 | 369 | 1.000 | \mathcal{E}_{\mathbb{R}}=\mathcal{E}_{\mathbb{R}}(\tilde{m} g) | | |
| cardona-qft-methods_FO3656 | 369 | 1.000 | \xi \in \mathcal{H} | | |
| cardona-qft-methods_FO3657 | 369 | 1.000 | g \xi | | |
| cardona-qft-methods_FO3658 | 369 | 1.000 | \pi(g) \xi | | |
| cardona-qft-methods_FO3659 | 369 | 1.000 | C(G) | | |
| cardona-qft-methods_FO3660 | 369 | 1.000 | \nu \in \mathcal{H} | | |
| cardona-qft-methods_FO3661 | 369 | 0.693 | \mathcal{H}=\overline{\mathbb{C}[G] \nu} | | |
| cardona-qft-methods_FO3662 | 369 | 1.000 | g e_{\xi}=e_{g \xi} | | |
| cardona-qft-methods_FO3663 | 369 | 1.000 | \xi \mapsto e_{\xi} | | |
| cardona-qft-methods_FO3664 | 369 | 1.000 | g \mapsto\langle g \nu, \xi\rangle | | |
| cardona-qft-methods_FO3665 | 369 | 0.996 | \left\{: e_{\xi} \mid \xi \in \mathcal{H}:\right\} | | |
| cardona-qft-methods_FO3666 | 369 | 1.000 | e_{\xi} | | |
| cardona-qft-methods_FO3667 | 369 | 1.000 | g H | | |
| cardona-qft-methods_FO3668 | 370 | 1.000 | \mathcal{H}^{\infty}=\mathcal{H}^{\infty}(\pi) \subseteq \mathcal{H} | | |
| cardona-qft-methods_FO3669 | 370 | 0.964 | g \in G \mapsto \pi(g) \xi \in \mathcal{H} | | |
| cardona-qft-methods_FO3670 | 370 | 1.000 | X \in \tilde{m} g | | |
| cardona-qft-methods_FO3671 | 370 | 1.000 | \xi \in \mathcal{H}^{\infty} | | |
| cardona-qft-methods_FO3672 | 370 | 1.000 | \exp : \tilde{m} g \rightarrow G | | |
| cardona-qft-methods_FO3673 | 370 | 1.000 | \mathbb{D} \pi | | |
| cardona-qft-methods_FO3674 | 370 | 1.000 | \mathcal{H}^{\infty} | | |
| cardona-qft-methods_FO3675 | 370 | 1.000 | \left\{e_{\xi} \mid \xi \in \mathcal{H}^{\infty}\right\} | | |
| cardona-qft-methods_FO3676 | 370 | 1.000 | g H \in M \mapsto \epsilon^{t X} g H \in M | | |
| cardona-qft-methods_FO3677 | 370 | 1.000 | \left.X \mapsto \mathbb{D} \pi(X)\right|_{\mathcal{F}} | | |
| cardona-qft-methods_FO3678 | 370 | 1.000 | \mathcal{F} \subseteq \mathcal{H}^{\infty}(\pi) | | |
| cardona-qft-methods_FO3679 | 370 | 0.998 | \left.\mathbb{1} \pi(X)\right|_{\mathcal{F}} | | |
| cardona-qft-methods_FO3680 | 370 | 1.000 | \mathbb{D} \pi(X) | | |
| cardona-qft-methods_FO3681 | 370 | 1.000 | \left.\mathbb{D} \pi(X)\right|_{\mathcal{F}} | | |
| cardona-qft-methods_FO3682 | 370 | 1.000 | { }^{\mathrm{a}} \mathcal{H}^{\infty} | | |
| cardona-qft-methods_FO3683 | 371 | 1.000 | \mathcal{L}^{\dagger}(\mathcal{F}) | | |
| cardona-qft-methods_FO3684 | 371 | 1.000 | \mathcal{F} \rightarrow \mathcal{F} | | |
| cardona-qft-methods_FO3685 | 371 | 1.000 | \mathcal{F} \subseteq \operatorname{dom}\left(A^{*}\right) | | |
| cardona-qft-methods_FO3686 | 371 | 1.000 | A^{\dagger}=\left.A^{*}\right|_{\mathcal{F}} | | |
| cardona-qft-methods_FO3687 | 371 | 1.000 | \mathcal{C}^{*}(\mathcal{F}) | | |
| cardona-qft-methods_FO3688 | 371 | 1.000 | \left.A\right|_{\mathcal{F}} \in \mathcal{L}^{\dagger}(\mathcal{F}) | | |
| cardona-qft-methods_FO3689 | 371 | 1.000 | \pi: \mathcal{A} \rightarrow \mathcal{L}^{\dagger}(\mathcal{F}) | | |
| cardona-qft-methods_FO3690 | 371 | 1.000 | \nu \in \mathcal{F} | | |
| cardona-qft-methods_FO3691 | 371 | 1.000 | \mathcal{F}=\mathcal{A} \nu | | |
| cardona-qft-methods_FO3692 | 371 | 1.000 | A^{\dagger} A | | |
| cardona-qft-methods_FO3693 | 371 | 1.000 | \mathcal{A}^{\dagger} | | |
| cardona-qft-methods_FO3694 | 371 | 1.000 | \omega \in \mathcal{A}^{\dagger} | | |
| cardona-qft-methods_FO3695 | 371 | 1.000 | \|\nu\|=1 | | |
| cardona-qft-methods_FO3696 | 371 | 0.999 | \left.\pi\right|_{\mathcal{A} \nu} | | |
| cardona-qft-methods_FO3697 | 372 | 1.000 | \mathcal{I}=\left\{A \in \mathcal{A} \mid \omega\left(A^{\dagger} A\right)=0\right\} | | |
| cardona-qft-methods_FO3698 | 372 | 1.000 | \mathcal{I} | | |
| cardona-qft-methods_FO3699 | 372 | 1.000 | \mathcal{F}=\mathcal{A} / \mathcal{I} | | |
| cardona-qft-methods_FO3700 | 372 | 1.000 | \nu=[1] \in \mathcal{F} | | |
| cardona-qft-methods_FO3701 | 372 | 1.000 | \pi: \mathcal{E} \rightarrow \mathcal{L}^{\dagger}(\mathcal{F}) | | |
| cardona-qft-methods_FO3702 | 372 | 0.903 | E \in \mathcal{E} | | |
| cardona-qft-methods_FO3703 | 372 | 0.903 | \operatorname{cl}(E) | | |
| cardona-qft-methods_FO3704 | 372 | 0.611 | c l(E+F)=c l(E)+c l(F) | | |
| cardona-qft-methods_FO3705 | 372 | 0.887 | \operatorname{cl}(E F)=\operatorname{cl}(E) \operatorname{cl}(F) | | |
| cardona-qft-methods_FO3706 | 372 | 0.644 | \operatorname{cl}\left(E^{\dagger}\right)=\operatorname{cl}(E)^{*} | | |
| cardona-qft-methods_FO3707 | 372 | 0.963 | c l\left(1+E^{\dagger} E\right) | | |
| cardona-qft-methods_FO3708 | 372 | 1.000 | \mathcal{E} \mathcal{S}^{-1} | | |
| cardona-qft-methods_FO3709 | 373 | 1.000 | \tilde{\mathcal{E}} \supseteq \mathcal{E} | | |
| cardona-qft-methods_FO3710 | 373 | 1.000 | \tilde{\mathcal{F}} \supseteq \mathcal{F} | | |
| cardona-qft-methods_FO3711 | 373 | 1.000 | \tilde{\mathcal{E}} | | |
| cardona-qft-methods_FO3712 | 373 | 1.000 | \mathcal{C}^{*}(\tilde{\mathcal{F}}) | | |
| cardona-qft-methods_FO3713 | 373 | 1.000 | \tilde{\mathcal{F}} \subseteq \mathcal{H} | | |
| cardona-qft-methods_FO3714 | 373 | 0.943 | \tilde{\mathcal{E}}=\mathcal{E} | | |
| cardona-qft-methods_FO3715 | 373 | 1.000 | \mathcal{E}^{\dagger} | | |
| cardona-qft-methods_FO3716 | 373 | 1.000 | \Delta: \mathcal{E} \rightarrow \mathcal{E} \otimes \mathcal{E} | | |
| cardona-qft-methods_FO3717 | 373 | 1.000 | \mathcal{T}(\tilde{m} g) | | |
| cardona-qft-methods_FO3718 | 373 | 1.000 | \mathcal{I} \subseteq \mathcal{T}(\tilde{m} g) | | |
| cardona-qft-methods_FO3719 | 373 | 1.000 | X Y-Y X-[X, Y] | | |
| cardona-qft-methods_FO3720 | 373 | 1.000 | X, Y \in \tilde{m} g | | |
| cardona-qft-methods_FO3721 | 373 | 1.000 | \mathcal{E}=\mathcal{T}(\tilde{m} g) / \mathcal{I} | | |
| cardona-qft-methods_FO3722 | 374 | 1.000 | \left(X_{1}, \ldots, X_{n}\right) | | |
| cardona-qft-methods_FO3723 | 374 | 1.000 | X^{\alpha}=X_{1}^{\alpha_{1}} \cdots X_{n}^{\alpha_{n}} | | |
| cardona-qft-methods_FO3724 | 374 | 0.998 | \binom{\alpha}{\beta}=\frac{\alpha!}{\beta!(\alpha-\beta)!}=\binom{\alpha_{1}}{\beta_{1}} \cdots\binom{\alpha_{d}}{\beta_{d}} | | |
| cardona-qft-methods_FO3725 | 374 | 1.000 | E \otimes F \mapsto F \otimes E | | |
| cardona-qft-methods_FO3726 | 374 | 1.000 | E, F \in \mathcal{E} | | |
| cardona-qft-methods_FO3727 | 374 | 1.000 | \tilde{m} g \rightarrow \operatorname{der}\left(\mathcal{E}^{\dagger}\right) | | |
| cardona-qft-methods_FO3728 | 374 | 0.999 | \operatorname{der}\left(\mathcal{E}^{\dagger}\right) | | |
| cardona-qft-methods_FO3729 | 374 | 0.999 | \delta: \mathcal{E}^{\dagger} \rightarrow \mathcal{E}^{\dagger} | | |
| cardona-qft-methods_FO3730 | 374 | 1.000 | a, b \in \mathcal{E}^{\dagger} | | |
| cardona-qft-methods_FO3731 | 375 | 1.000 | X_{1}, \ldots, X_{n} | | |
| cardona-qft-methods_FO3732 | 375 | 1.000 | \mathcal{E}^{\dagger} \cong | | |
| cardona-qft-methods_FO3733 | 375 | 1.000 | \mathbb{C} \llbracket x_{1}, \ldots, x_{n} \rrbracket | | |
| cardona-qft-methods_FO3734 | 375 | 1.000 | 1 \in \mathcal{E} | | |
| cardona-qft-methods_FO3735 | 375 | 1.000 | \chi_{0} | | |
| cardona-qft-methods_FO3736 | 375 | 1.000 | a \in \mathcal{E}^{\dagger} | | |
| cardona-qft-methods_FO3737 | 375 | 1.000 | E \in \mathcal{E},(E a)^{\dagger}=\bar{E} a^{\dagger} | | |
| cardona-qft-methods_FO3738 | 375 | 1.000 | E, F \in \mathcal{E}_{\mathbb{R}} | | |
| cardona-qft-methods_FO3739 | 375 | 1.000 | (E a)^{\dagger}(F)=\overline{a\left(E^{\dagger} F\right)}=E a^{\dagger}(F) | | |
| cardona-qft-methods_FO3740 | 376 | 1.000 | J \nu=\nu | | |
| cardona-qft-methods_FO3741 | 376 | 1.000 | \left\{e_{\xi} \mid \xi \in \mathcal{F}\right\} | | |
| cardona-qft-methods_FO3742 | 376 | 1.000 | \chi_{0} \in M | | |
| cardona-qft-methods_FO3743 | 376 | 1.000 | \xi \in \mathcal{H} \backslash \mathcal{F} | | |
| cardona-qft-methods_FO3744 | 376 | 1.000 | E \in \mathcal{E}, E e_{\xi} | | |
| cardona-qft-methods_FO3745 | 376 | 1.000 | e_{\eta} | | |
| cardona-qft-methods_FO3746 | 376 | 1.000 | \eta \in \mathcal{H} | | |
| cardona-qft-methods_FO3747 | 376 | 1.000 | E e_{\xi}=e_{E \xi} | | |
| cardona-qft-methods_FO3748 | 376 | 1.000 | \xi \in \mathcal{F} | | |
| cardona-qft-methods_FO3749 | 376 | 1.000 | F \in \mathcal{E} | | |
| cardona-qft-methods_FO3750 | 376 | 1.000 | \omega \in \mathcal{E}^{\dagger} | | |
| cardona-qft-methods_FO3751 | 377 | 1.000 | \mathcal{E}^{\dagger} \cong \mathbb{C} \llbracket x_{1}, \ldots, x_{n} \rrbracket | | |
| cardona-qft-methods_FO3752 | 377 | 1.000 | \chi_{0}(a)=a(1) | | |
| cardona-qft-methods_FO3753 | 377 | 1.000 | \omega \cong \cos (x) | | |
| cardona-qft-methods_FO3754 | 377 | 1.000 | X \omega | | |
| cardona-qft-methods_FO3755 | 377 | 1.000 | \mathcal{A} \cong \mathbb{C}[u, v] /\left(u^{2}+v^{2}-1\right) | |