Remarks on nonlinear Electrodynamics

TL;DR

This paper explores nonlinear electrodynamics models, showing that Born-Infeld-like theories produce finite field energy for point charges and both models exhibit vacuum birefringence, with modifications to Coulomb potential and ultraviolet finiteness in non-commutative versions.

Contribution

It analyzes generalized Born-Infeld and Exponential Electrodynamics, deriving long-range corrections to Coulomb potential and demonstrating finiteness in non-commutative cases.

Findings

Finite field energy for point charges in Born-Infeld-like models

Vacuum birefringence observed in both models

Long-range $1/r^5$ corrections to Coulomb potential

Abstract

We consider both generalized Born-Infeld and Exponential Electrodynamics. The field-energy of a point-like charge is finite only for Born-Infeld-like Electrodynamics. However, both Born-Infeld-type and Exponential Electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of Electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in long-range ($1/r^5$- type) corrections to the Coulomb potential. Once again, for their non-commutative versions, the interaction energy is ultraviolet finite.