Nonlinear corrections in basic problems of electro- and magneto-statics in the vacuum

TL;DR

This paper calculates third-order nonlinear corrections to electrostatic and magnetostatic fields in vacuum using QED, showing that these corrections can account for discrepancies in baryon magnetic moments.

Contribution

It introduces a method to compute nonlinear corrections to static fields in QED using the polarization tensor within the local approximation.

Findings

Nonlinear corrections to Coulomb and dipole fields are derived.

The nonlinear correction to baryon magnetic moments matches experimental-theoretical gaps.

Results are applicable to weakly varying fields in vacuum.

Abstract

We find third-power nonlinear corrections to the Coulomb and other static electric fields, as well as to the electric and magnetic dipole fields, as we work within QED with no background field. The nonlinear response function we base our consideration on is the fourth-rank polarization tensor, calculated within the local (infrared) approximation of the effective action. Therefore, the results are applicable to weakly varying fields. It is established that the nonlinear correction to magnetic moment of some baryons just matches, in the order of magnitude, the existing gap between its experimental and theoretical values.