Remarks on nonlinear electrodynamics II

TL;DR

This paper investigates nonlinear electrodynamics models in strong fields, revealing vacuum birefringence and calculating modifications to Coulomb potential, including novel long-range corrections and finiteness in non-commutative cases.

Contribution

It introduces new long-range corrections to the Coulomb potential in massive Euler-Heisenberg-like electrodynamics and analyzes their properties in strong-field regimes.

Findings

Massive Euler-Heisenberg-like electrodynamics exhibits vacuum birefringence.

New long-range ($1/r^3$) and ($1/r^5$) corrections to Coulomb potential are identified.

Interaction energy in non-commutative versions is ultraviolet finite.

Abstract

We consider both massive Euler-Heisenberg-like and Euler-Heisenberg-like Electrodynamics in the approximation of the strong-field limit. Our analysis shows that massive Euler-Heisenberg-type Electrodynamics displays the vacuum birefringence phenomenon. Afterwards, 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. Interestingly enough, for massive Euler-Heisenbeg-like electrodynamics (Whichmann-Kroll) we obtain a new long-range ($1/r^3$- type) correction, apart from a long-range ($1/r^5$- type) correction to the Coulomb potential. However, Euler-Heisenberg-like Electrodynamics in the approximation of the strong-field limit (to the leading logarithmic order), display a long-range ($1/r^5$- type) correction to the Coulomb potential. Again, for their non-commutative versions, the interaction energy is ultraviolet finite.