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This article is cited in 31 scientific papers (total in 31 papers)
Classical and Quantum Dilogarithm Identities
Rinat M. Kashaeva, Tomoki Nakanishib a Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland
b Graduate School of Mathematics, Nagoya University, Nagoya, 464-8604, Japan
Abstract:
Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We then demonstrate how classical dilogarithm identities naturally emerge from quantum dilogarithm identities in local form in the semiclassical limit by applying the saddle point method.
Keywords:
dilogarithm, quantum dilogarithm, cluster algebra.
Received: May 3, 2011; in final form October 26, 2011; Published online November 1, 2011
Citation:
Rinat M. Kashaev, Tomoki Nakanishi, “Classical and Quantum Dilogarithm Identities”, SIGMA, 7 (2011), 102, 29 pp.
Linking options:
https://www.mathnet.ru/eng/sigma660 https://www.mathnet.ru/eng/sigma/v7/p102
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Abstract page: | 318 | Full-text PDF : | 109 | References: | 44 |
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