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.
Classical and Quantum Dilogarithm Identities
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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.
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Heisenberg-Euler and the Quantum Dilogarithm
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.