Dual symmetry in a generalized Maxwell theory

TL;DR

This paper explores a generalized Maxwell theory, introducing a dual gauge field to restore dual symmetry, which is only fully achieved in the Maxwell limit, and discusses implications for electromagnetic invariants.

Contribution

It proposes a generalized duality transformation in Podolsky's electrodynamics, restoring dual symmetry through a dual gauge field and analyzing its implications.

Findings

Dual symmetry is restored asymptotically in the Maxwell limit.

A generalized Hodge duality leads to a dual gauge field.

Dual symmetry implies invariants of electromagnetic fields.

Abstract

We examine Podolsky's electrodynamics, which is noninvariant under the usual duality transformation. We deduce a generalization of Hodge's star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry. The model becomes fully dual symmetric asymptotically when it reduces to the Maxwell theory. We argue that this strict dual symmetry directly implies the existence of the basic invariants of the electromagnetic fields.