A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited

TL;DR

This paper develops a non-local action for electrodynamics based on fields rather than potentials, exploring duality symmetry and the Aharonov-Bohm effect in a novel, non-local framework.

Contribution

It refines a non-local action formalism for electrodynamics and offers new insights into duality symmetry and the Aharonov-Bohm effect using this approach.

Findings

Derives electric-magnetic duality from vacuum electrodynamics as a harmonic oscillator.

Shows the magnetic Aharonov-Bohm effect arises naturally in a non-local formalism.

Provides a novel perspective on subtle electromagnetic phenomena.

Abstract

A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov--Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner.