Born-Infeld electrodynamics in very special relativity

TL;DR

This paper explores a modified Born-Infeld electrodynamics within very special relativity, revealing a massive dispersion relation and a novel long-range correction to the Coulomb potential, highlighting new effects of VSR on nonlinear electrodynamics.

Contribution

It introduces a VSR-invariant nonlinear electrodynamics model and analyzes its electrostatic solutions, dispersion relations, and potential corrections, revealing unique long-range effects.

Findings

VSR induces a massive dispersion relation in nonlinear electrodynamics.

A new long-range $1/L^3$ correction to Coulomb potential is found.

Electrostatic solutions exhibit VSR mass effects in gauge-invariant context.

Abstract

In this work we discuss the properties of a modified Born-Infeld electrodynamics in the framework of very special relativity (VSR). This proposal allows us to study VSR mass effects in a gauge-invariant context of nonlinear electrodynamics. It is analyzed in detail the electrostatic solutions for two different cases, as well as the VSR dispersion relations are found to be of a \emph{massive} particle with nonlinear modifications. Afterwards, the field energy and static potential are computed, in the latter we find from the VSR contribution a novel long-range $1/L^3$ correction to the Coulomb potential, in contrast to the $1/L^5$ correction of the usual Born-Infeld theory.