Nonlinear magnetic response of the magnetized vacuum to applied electric field

TL;DR

This paper derives the first nonlinear correction to the magnetic field caused by a static charge in a constant magnetic background, using a model-independent approach within nonlinear electrodynamics including QED.

Contribution

It provides a general, model-independent formula for the nonlinear magnetic response of the vacuum to a static charge in a magnetic field, extending previous linear analyses.

Findings

Nonlinear correction is quadratic in charge and purely magnetic.

Response function is expressed within the local approximation of the effective action.

Results are applicable to any P-invariant nonlinear electrodynamics, including QED.

Abstract

We find first nonlinear correction to the field, produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor - the nonlinear response function - is written within the local approximation of the effective action in an otherwise model- and approximation-independent way within any P-invariant nonlinear electrodynamics, QED included.