Heisenberg-Euler and the Quantum Dilogarithm

Fuente: arXiv
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Main Author: Dunne, Gerald V.
Format: Preprint
Published: 2025
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author Dunne, Gerald V.
author_facet Dunne, Gerald V.
contents A dispersion integral representation of the Heisenberg-Euler QED effective lagrangian is derived, with Faddeev's quantum dilogarithm as a generalized Borel kernel. The nonperturbative imaginary part of the effective lagrangian is expressed as the quantum dilogarithm, while the real part has the form of a dispersion integral involving both the quantum dilogarithm and its modular dual, a manifestation of electromagnetic duality. The Heisenberg-Euler effective lagrangian generates all one-loop QED scattering amplitudes in a constant external field, with the Lorentz invariants of the constant background electromagnetic field playing the role of the Mandelstam variables in conventional QED dispersion theory.
format Preprint
id arxiv_https___arxiv_org_abs_2512_14915
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Heisenberg-Euler and the Quantum Dilogarithm
Dunne, Gerald V.
High Energy Physics - Theory
High Energy Physics - Phenomenology
Mathematical Physics
A dispersion integral representation of the Heisenberg-Euler QED effective lagrangian is derived, with Faddeev's quantum dilogarithm as a generalized Borel kernel. The nonperturbative imaginary part of the effective lagrangian is expressed as the quantum dilogarithm, while the real part has the form of a dispersion integral involving both the quantum dilogarithm and its modular dual, a manifestation of electromagnetic duality. The Heisenberg-Euler effective lagrangian generates all one-loop QED scattering amplitudes in a constant external field, with the Lorentz invariants of the constant background electromagnetic field playing the role of the Mandelstam variables in conventional QED dispersion theory.
title Heisenberg-Euler and the Quantum Dilogarithm
topic High Energy Physics - Theory
High Energy Physics - Phenomenology
Mathematical Physics
url https://arxiv.org/abs/2512.14915