"Modular quantum dilogarithm"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| 4번째 줄: | 4번째 줄: | ||
* applications | * applications | ||
** [[S-matrix of the quantum sine-Gordon model]] | ** [[S-matrix of the quantum sine-Gordon model]] | ||
| − | * definition : | + | * definition : <math>b\in \mathbb{C}</math> with non-zero real part and <math>z\in \mathbb{C}</math> |
| − | + | :<math> | |
\Phi_{b}(z)=\exp\left(-\frac{1}{4}\int \frac{e^{-2zx\sqrt{-1}}}{\sinh(xb) \sinh(x/b)}\, \frac{dx}{x}\right) | \Phi_{b}(z)=\exp\left(-\frac{1}{4}\int \frac{e^{-2zx\sqrt{-1}}}{\sinh(xb) \sinh(x/b)}\, \frac{dx}{x}\right) | ||
| − | + | </math> | |
==properties== | ==properties== | ||
| 27번째 줄: | 27번째 줄: | ||
==articles== | ==articles== | ||
* D. Chicherin, V. P. Spiridonov, The hyperbolic modular double and Yang-Baxter equation, arXiv:1511.00131 [math-ph], October 31 2015, http://arxiv.org/abs/1511.00131 | * D. Chicherin, V. P. Spiridonov, The hyperbolic modular double and Yang-Baxter equation, arXiv:1511.00131 [math-ph], October 31 2015, http://arxiv.org/abs/1511.00131 | ||
| − | * Ip, Ivan C. H. “On Tensor Product Decomposition of Positive Representations of | + | * Ip, Ivan C. H. “On Tensor Product Decomposition of Positive Representations of <math>\mathcal{U}_{q\tilde{q}}(\mathfrak{sl}(2,\mathbb{R}))</math>.” arXiv:1511.07970 [math], November 25, 2015. http://arxiv.org/abs/1511.07970. |
* Chicherin, D., and V. P. Spiridonov. “The Hyperbolic Modular Double and Yang-Baxter Equation.” arXiv:1511.00131 [hep-Th, Physics:math-Ph], October 31, 2015. http://arxiv.org/abs/1511.00131. | * Chicherin, D., and V. P. Spiridonov. “The Hyperbolic Modular Double and Yang-Baxter Equation.” arXiv:1511.00131 [hep-Th, Physics:math-Ph], October 31, 2015. http://arxiv.org/abs/1511.00131. | ||
* Chicherin, D., and S. Derkachov. ‘Matrix Factorization for Solutions of the Yang-Baxter Equation’. arXiv:1502.07923 [hep-Th, Physics:math-Ph], 27 February 2015. http://arxiv.org/abs/1502.07923. | * Chicherin, D., and S. Derkachov. ‘Matrix Factorization for Solutions of the Yang-Baxter Equation’. arXiv:1502.07923 [hep-Th, Physics:math-Ph], 27 February 2015. http://arxiv.org/abs/1502.07923. | ||
2020년 11월 16일 (월) 05:34 판
introduction
- introduced by Ludvig Faddeev
- called the modular quantum dilogarithm or regularized quantum dilogarithm
- applications
- definition \[b\in \mathbb{C}\] with non-zero real part and \(z\in \mathbb{C}\)
\[ \Phi_{b}(z)=\exp\left(-\frac{1}{4}\int \frac{e^{-2zx\sqrt{-1}}}{\sinh(xb) \sinh(x/b)}\, \frac{dx}{x}\right) \]
properties
symmetries
recurrence relation
unitarity
relation with other quantum dilogarithms
articles
- D. Chicherin, V. P. Spiridonov, The hyperbolic modular double and Yang-Baxter equation, arXiv:1511.00131 [math-ph], October 31 2015, http://arxiv.org/abs/1511.00131
- Ip, Ivan C. H. “On Tensor Product Decomposition of Positive Representations of \(\mathcal{U}_{q\tilde{q}}(\mathfrak{sl}(2,\mathbb{R}))\).” arXiv:1511.07970 [math], November 25, 2015. http://arxiv.org/abs/1511.07970.
- Chicherin, D., and V. P. Spiridonov. “The Hyperbolic Modular Double and Yang-Baxter Equation.” arXiv:1511.00131 [hep-Th, Physics:math-Ph], October 31, 2015. http://arxiv.org/abs/1511.00131.
- Chicherin, D., and S. Derkachov. ‘Matrix Factorization for Solutions of the Yang-Baxter Equation’. arXiv:1502.07923 [hep-Th, Physics:math-Ph], 27 February 2015. http://arxiv.org/abs/1502.07923.
- Garoufalidis, Stavros, and Rinat Kashaev. ‘Evaluation of State Integrals at Rational Points’. arXiv:1411.6062 [hep-Th], 21 November 2014. http://arxiv.org/abs/1411.6062.
- Faddeev, Ludwig D., and Leon A. Takhtajan. “On the Spectral Theory of One Functional-Difference Operator from Conformal Field Theory.” arXiv:1408.0307 [hep-Th, Physics:math-Ph], August 1, 2014. http://arxiv.org/abs/1408.0307.
- http://arxiv.org/abs/1305.4291
- Johnson, P. R. 1996. “Exact Quantum S-matrices for Solitons in Simply-laced Affine Toda Field Theories.” arXiv:hep-th/9611117 (November 15). doi:10.1016/S0550-3213(97)00239-3. http://arxiv.org/abs/hep-th/9611117.
- Faddeev, L. 1995. “Discrete Heisenberg-Weyl Group and Modular Group.” arXiv:hep-th/9504111 (April 21). doi:10.1007/BF01872779. http://arxiv.org/abs/hep-th/9504111.
- Faddeev, L. D. 1994. “Current-Like Variables in Massive and Massless Integrable Models.” arXiv:hep-th/9408041 (August 7). http://arxiv.org/abs/hep-th/9408041.