A non-linear duality-invariant conformal extension of Maxwell's equations

TL;DR

This paper derives all nonlinear, duality- and conformally-invariant extensions of Maxwell's equations, revealing a new weak-field limit with unique wave properties, including birefringence and exact plane-wave solutions.

Contribution

It identifies all such nonlinear extensions as limits of a generalized Born-Infeld theory, introducing a novel weak-field regime with distinctive wave phenomena.

Findings

Weak-field limit differs from classical Maxwell theory

Existence of exact light-velocity plane-wave solutions

Presence of birefringence in small-amplitude waves

Abstract

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarisation. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarisation mode remains lightlike.