Elecromagnetic Duality on the Light-Front in the Presence of External Sources

TL;DR

This paper explores electromagnetic duality on the light-front within Zwanziger's framework, demonstrating that the duality transformation preserves the Hamiltonian density even with external magnetic sources.

Contribution

It extends the understanding of electromagnetic duality to the light-front formalism with external sources, showing invariance of the Hamiltonian under duality transformations.

Findings

Duality transformation similar to Susskind's for free theory

Hamiltonian density remains invariant under duality

Two independent phase space degrees of freedom identified

Abstract

We investigate the issue of electromagnetic duality on the light front. We work with Zwanziger's theory of electric and magnetic sources which is appropriate for treating duality. When quantized on the light-front in the light front gauge, this theory yields two independent phase space degrees of freedom, namely the two transverse field components, the right number to describe the gauge field sector of normal light-front QED and also the appropriate commutator between them. The electromagnetic duality transformation formulated in terms of them is similar in form to the Susskind transformation proposed for the free theory, provided one identifies them as the dynamical field components of the photon on the light-front in the presence of magnetic sources. The Hamiltonian density written in terms of these components is invariant under the duality transformation.