Nonlinear Electromagnetic Self-Duality and Legendre Transformations

TL;DR

This paper explores the properties of electromagnetic theories with duality symmetries, focusing on nonlinear self-duality and the role of Legendre transformations in relating different formulations.

Contribution

It provides a detailed analysis of continuous duality transformations and their connection to Legendre transformations in nonlinear electromagnetic theories.

Findings

Discrete duality elements relate to Legendre transformations.

Duality invariance constrains the form of electromagnetic interactions.

Scalar field cases illustrate the duality properties.

Abstract

We discuss continuous duality transformations and the properties of classical theories with invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. Special discrete elements of the continuous group are shown to be related to the Legendre transformation with respect to the field strengths.