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Classical and Quantum Dilogarithm Identities

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arxiv 1104.4630 v4 pith:YTIWLVOU submitted 2011-04-24 math.QA math.RA

Classical and Quantum Dilogarithm Identities

Rinat M. Kashaev , Tomoki Nakanishi This is my paper
classification math.QA math.RA
keywords quantumdilogarithmidentitiesclassicalclusterformslocalalgebra
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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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  1. Heisenberg-Euler and the Quantum Dilogarithm

    hep-th 2025-12 conditional novelty 7.0

    Heisenberg-Euler effective Lagrangian is recast as a dispersion integral with the quantum dilogarithm as kernel, its imaginary part given directly by the dilogarithm and its real part involving the modular dual.