"Modular quantum dilogarithm"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
==introduction== | ==introduction== | ||
| − | * introduced by | + | * introduced by Faddeev |
* called the modular quantum dilogarithm or regularized quantum dilogarithm | * called the modular quantum dilogarithm or regularized quantum dilogarithm | ||
* applications | * applications | ||
** [[S-matrix of the quantum sine-Gordon model]] | ** [[S-matrix of the quantum sine-Gordon model]] | ||
| + | * 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=== | ||
2013년 4월 7일 (일) 12:30 판
introduction
- introduced by 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
- 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.