On the role of induced electric field in the time-dependent Aharonov-Bohm effect

TL;DR

This paper re-examines the long-standing debate on the existence of the time-dependent Aharonov-Bohm effect, emphasizing the crucial role of induced electric fields and their impact on the phase shift.

Contribution

It provides a detailed analysis of the induced electric field's role, clarifying its effect on the time-dependent AB effect and aiding in its experimental verification.

Findings

Induced electric fields significantly influence the AB phase shift.

Careful treatment of time-varying vector potentials is essential.

The analysis supports the potential observability of the time-dependent AB effect.

Abstract

Whether the time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate. There are two factors complicating the problem. First, in the closed spacetime line integral of the vector potential that is thought to give the AB-phase shift, how to treat the time-varying vector potential is highly nontrivial. Second, the time-varying magnetic flux generates induced electric field even outside the solenoid. In the present paper, motivated by a recent work by Gao, we re-investigate the role of the induced electric field with the utmost care. This analysis reveals a highly nontrivial effect of the induced electric field, which turns out to be useful for verifying the very existence of the time-dependent AB-effect.