Induced electromagnetic fields in non-linear QED

TL;DR

This paper derives general formulas for electromagnetic fields induced by non-linear quantum electrodynamics effects, specifically using the Euler-Heisenberg Lagrangian, and applies them to a charged spherical shell in a magnetic field.

Contribution

It provides new analytical expressions for induced fields in non-linear QED and demonstrates their application to a spherical shell with uniform charge in a magnetic background.

Findings

Induced electric fields have complex multipole structures.

Leading induced magnetic field is due to an induced magnetic dipole moment.

Expressions are valid for quasistatic, leading-order non-linear regimes.

Abstract

The Euler-Heisenberg effective Lagrangian is used to obtain general expressions for electric and magnetic fields induced by non-linearity, to leading order in the non-linear expansion parameter, and for quasistatic situations. These expressions are then used to compute the induced electromagnetic fields due to a spherical shell with uniform charge distribution on the surface, in the presence of an external constant magnetic field. The induced electric field contains several multipole terms with unusual angular dependences. Most importantly, the leading term of the induced magnetic field is due to an induced magnetic dipole moment.