Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories

TL;DR

This paper systematically explores nonlinear and higher derivative extensions of electromagnetism, clarifying the derivation of action functionals, and generalizing Schroedinger's formulation to these theories, revealing hidden algebraic structures.

Contribution

It provides a general framework for deriving action functionals from nonlinear equations and extends Schroedinger's formulation to nonlinear and higher derivative electromagnetic theories.

Findings

Established when action functionals can be explicitly obtained.

Generalized Schroedinger's formulation to nonlinear theories.

Discovered a hidden quartic equation in duality conditions.

Abstract

We present a systematic study of nonlinear and higher derivatives extensions of electromagnetism. We clarify when action functionals S[F] can be explicitly obtained from arbitrary (not necessarily self-dual) nonlinear equations of motion. We show that the "Deformed twisted self-duality condition" proposal originated in the context of supergravity counterterms is actually the general framework needed to discuss self-dual theories starting from a variational principle. We generalize to nonlinear and higher derivatives theories Schroedinger formulation of Born-Infeld theory, and for the latter, and more in general for nonlinear theories, we derive a closed form expression of the corresponding deformed twisted self-duality conditions. This implies that the hypergeometric expression entering these duality conditions and leading to Born-Infeld theory satisfies a hidden quartic equation.