Combined Electric and Magnetic Aharonov-Bohm Effects

TL;DR

This paper demonstrates a unified configuration illustrating both electric and magnetic Aharonov-Bohm effects, emphasizing the gauge-invariance of their combined phase in a relativistic framework.

Contribution

It introduces a novel setup that combines electric and magnetic Aharonov-Bohm effects in a single configuration, highlighting gauge-invariance of the total phase.

Findings

The phases depend on the particle's path and are gauge-dependent individually.

The sum of the electric and magnetic phases is gauge-invariant.

The scheme is pedagogically useful for understanding gauge invariance in quantum phases.

Abstract

It is well-known that the electric and magnetic Aharonov-Bohm effects may be formally described on equal footing using the four-vector potential in a relativistic framework. We propose an illustrative manifestation of both effects in a single configuration, in which the specific path of the charged particle determines the weight of the electric and magnetic acquired relative phases. The phases can be distinctively obtained in the Coulomb gauge. The scheme manifests the pedagogical lesson that though each of the relative phases is gauge-dependent their sum is gauge-invariant.