Classical and Quantum Dilogarithm Identities

Details Classical and Quantum Dilogarithm Identities Classical and Quantum Dilogarithm Identities

2011-04-24

arxiv.org/abs/1104.4630v4

SIGMA 7 (2011), 102, 29 pages

Mathematics

Quantum Algebra

Scientific paper

10.3842/SIGMA.2011.102

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.

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