Aharonov-Bohm Effect in Generalized Electrodynamics

TL;DR

This paper explores the Aharonov-Bohm effect within Generalized Electrodynamics, revealing how massive photon modes introduce measurable corrections to the phase shift, which could help constrain the photon mass experimentally.

Contribution

It demonstrates the impact of massive photon modes in Generalized Electrodynamics on the AB phase shift, extending the understanding beyond Maxwell's theory.

Findings

Massless mode recovers the standard AB phase shift.

Massive mode introduces a correction factor to the phase shift.

Potential for experimental constraints on photon mass.

Abstract

The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally {\normalsize{}U(1)}-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.