Work

Heisenberg-Euler and the quantum dilogarithm

Year: 2026

Type: article

Abstract: 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.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/ly3t-zp5l

Author: Gerald V. Dunne

Institution: University of Connecticut

Language: English

Topic: Quantum and Classical Electrodynamics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: U.S. Department of Energy, Office of Science, High Energy Physics

Awards: THEORETICAL HIGH ENERGY AND PARTICLE PHYSICS, G549135251, THEORETICAL HIGH ENERGY AND PARTICLE PHYSICS