Simplified self-dual electrodynamics

A bstract 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.