Simplified self-dual electrodynamics

TL;DR

This paper introduces a new formulation for self-dual nonlinear electrodynamics using auxiliary fields, simplifying the derivation of explicit Lagrangians for a broad class of theories, including generalizations of Born-Infeld.

Contribution

It provides a novel auxiliary-field approach that simplifies the construction of explicit Lagrangians for analytic self-dual electrodynamics theories.

Findings

Auxiliary-field potential determines interactions with causality.

Explicit Lagrangian obtained for even functions of auxiliary fields.

Generalizes Born-Infeld theory to all analytic self-dual theories.

Abstract

We present a new formulation of self-dual nonlinear electrodynamics in which interactions are determined by an auxiliary-field potential, with causality ensuring a unique solution to the auxiliary-field equation. The long-standing problem of an explicit Lagrangian for the generic `analytic' theory is simply solved by restriction to potentials that are even functions of the auxiliary field. In this case the Lagrangian can be linearised in quadratic field-strength scalars by the introduction of an additional pseudoscalar auxiliary field; this generalises, to all analytic self-dual theories, a well-known construction of the Born-Infeld theory.