Causal Self-Dual Electrodynamics

TL;DR

This paper demonstrates that for nonlinear electrodynamics theories, a unique causal and self-dual theory exists matching the weak-field Lagrangian, ensuring causality extends from weak to strong fields.

Contribution

The authors establish a method to construct a unique causal, self-dual nonlinear electrodynamics theory from any given weak-field Lagrangian, linking weak and strong field causality.

Findings

Existence of a unique causal, self-dual NLED for any weak-field Lagrangian.

Strong-field causality follows from weak-field causality in self-dual theories.

Explicit examples illustrating the construction and properties.

Abstract

Many theories of nonlinear electrodynamics (NLED) that have been proposed in physical contexts involving strong fields are causal for weak fields but acausal for strong fields. We show that for any such theory there is a unique causal and self-dual (electromagnetic duality invariant) theory with the same Lagrangian at zero magnetic field. This follows from a construction of the general causal self-dual NLED, which shows that strong-field causality is implied by weak-field causality for self-dual theories. We illustrate our results with explicit examples.