Nonlinear Electrodynamics without Birefringence

TL;DR

This paper classifies all nonlinear electrodynamics theories that do not exhibit birefringence, revealing new cases beyond Born-Infeld and Plebanski, and analyzing their limits and propagation properties.

Contribution

It systematically finds all solutions to no-birefringence conditions, including novel cases like reverse and extreme Born-Infeld, expanding the understanding of nonlinear electrodynamics.

Findings

Only Born-Infeld has a weak-field limit.

Only Born-Infeld and extreme-Born-Infeld avoid superluminal propagation.

All cases share a conformal strong-field limit similar to Born-Infeld.

Abstract

All solutions of the no-birefringence conditions for nonlinear electrodynamics are found. In addition to the known Born-Infeld and Plebanski cases, we find a ``reverse Born-Infeld'' case, which has a limit to Plebanski, and an ``extreme-Born-Infeld'' case, which arises as a Lagrangian constraint. Only Born-Infeld has a weak-field limit, and only Born-Infeld and extreme-Born Infeld avoid superluminal propagation in constant electromagnetic backgrounds, but all cases have a conformal strong-field limit that coincides with the strong-field limit of Born-Infeld found by Bialynicki-Birula.