Nonlinear electrodynamics without birefringence

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.

Automated summary

All solutions to the no-birefringence conditions in nonlinear electrodynamics have been discovered. Along with the known Born-Infeld and Plebanski cases, a reverse Born-Infeld case and an extreme-Born-Infeld case have been found. Only Born-Infeld has a weak-field limit, and only Born-Infeld and extreme-Born-Infeld prevent superluminal propagation in constant electromagnetic backgrounds. However, all cases have a conformal strong-field limit that coincides with the strong-field limit of Born-Infeld as found by Bialynicki-Birula.