Causal Self-Dual Electrodynamics

Many theories of nonlinear electrodynamics (NLED) that have been proposed inphysical contexts involving strong fields are causal for weak fields butacausal for strong fields. We show that for any such theory there is a uniquecausal and self-dual (electromagnetic duality invariant) theory with the sameLagrangian at zero magnetic field. This follows from a construction of thegeneral causal self-dual NLED, which shows that strong-field causality isimplied by weak-field causality for self-dual theories. We illustrate ourresults with explicit examples.