Gauge invariance of the local phase in the Aharonov-Bohm interference: quantum electrodynamic approach

TL;DR

This paper demonstrates the gauge invariance of the local phase shift in the magnetic Aharonov-Bohm effect using a quantum electrodynamic approach, addressing debates on locality and the role of potentials.

Contribution

It provides a microscopic, gauge-invariant analysis of the local phase in the magnetic Aharonov-Bohm effect, contrasting with semiclassical results and clarifying the issue of locality.

Findings

Gauge invariance of the local phase shift in magnetic AB effect confirmed

Quantum electrodynamics offers a microscopic understanding of the interaction

The electric AB effect involves additional complexities with virtual scalar photons

Abstract

In the Aharonov-Bohm (AB) effect, interference fringes are observed for a charged particle in the absence of the local overlap with the external electromagnetic field. This notion of the apparent nonlocality of the interaction or the significant role of the potential has recently been challenged and are under debate. The quantum electrodynamic approach provides a microscopic picture of the characteristics of the interaction between a charge and an external field. We explicitly show the gauge invariance of the local phase shift in the magnetic AB effect, which is in contrast to the results obtained using the usual semiclassical vector potential. Our study can resolve the issue of the locality in the magnetic AB effect. However, the problem is not solved in the same way in the electric counterpart wherein virtual scalar photons play an essential role.