QED Effective Action in Magnetic Field Backgrounds and Electromagnetic Duality

TL;DR

This paper develops a method using inverse scattering matrices to compute one-loop effective actions in magnetic backgrounds, demonstrating electromagnetic duality between electric and magnetic fields, including localized and uniform cases.

Contribution

It introduces a novel approach for calculating effective actions in magnetic fields and explores electromagnetic duality in various magnetic configurations.

Findings

Effective actions calculated for Sauter-type magnetic fields.

Demonstration of electromagnetic duality between electric and magnetic fields.

Approximate effective actions for general magnetic fields using semiclassical methods.

Abstract

In the in-out formalism we advance a method of the inverse scattering matrix for calculating effective actions in pure magnetic field backgrounds. The one-loop effective actions are found in a localized magnetic field of Sauter type and approximately in a general magnetic field by applying the uniform semiclassical approximation. The effective actions exhibit the electromagnetic duality between a constant electric field and a constant magnetic field and between $E(x) = E sech^2 (x/L)$ and $B(x) = B sech^2 (x/L)$.