Magnetic response from constant backgrounds to Coulomb sources

TL;DR

This paper investigates how a vacuum with constant electric and magnetic fields responds magnetically to a static electric charge, revealing induced magnetic effects and currents within nonlinear electrodynamics, especially in QED.

Contribution

It derives the magnetically uncharged linear response of the vacuum to a static charge in combined constant fields, including specific results for QED using the Heisenberg-Euler Lagrangian.

Findings

Response can be interpreted as two magnetic charges of opposite polarity at one point.

Coefficients for magnetic response are explicitly calculated within QED.

Induced currents and magnetic fields depend on external field configurations.

Abstract

Magnetically uncharged, magnetic linear response of the vacuum filled with arbitrarily combined constant electric and magnetic fields to an imposed static electric charge is found within general nonlinear electrodynamics. When the electric charge is point-like and external fields are parallel, the response found may be interpreted as a field of two point-like magnetic charges of opposite polarity in one point. Coefficients characterizing the magnetic response and induced currents are specialized to Quantum Electrodynamics, where the nonlinearity is taken as that determined by the Heisenberg-Euler effective Lagrangian.