English

Classical and Quantum Dilogarithm Identities

Quantum Algebra 2011-11-02 v4 Rings and Algebras

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

Cite

@article{arxiv.1104.4630,
  title  = {Classical and Quantum Dilogarithm Identities},
  author = {Rinat M. Kashaev and Tomoki Nakanishi},
  journal= {arXiv preprint arXiv:1104.4630},
  year   = {2011}
}
R2 v1 2026-06-21T17:58:11.863Z