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American Journal of Physics

A critical re-examination of the Aharonov–Bohm effect

Dipankar Home, S. Sengupta

Published Oct 1, 1983• 14 citations
Publisher

Abstract

The controversy concerning theoretical treatment of the Aharonov–Bohm (AB) effect is critically investigated. A new approach, taking the time-dependent aspect of this effect into consideration, is proposed which seeks to resolve the prevalent ambiguities. This provides interesting insight into the origin of the AB effect. Some clarifications are also made regarding the experimental verification of this effect.

DOI
10.1119/1.13391

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Reply to “Comment on ‘Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect' ”

R. Y. Chiao, Harold Hart, Michael Scheibner +4 more

We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.

Physical Review A•May 29, 2025•0 citations
The controversy concerning theoretical treatment of the Aharonov–Bohm (AB) effect is critically investigated. A new approach, taking the time-dependent aspect of this effect into consideration, is proposed which seeks to resolve the prevalent ambiguities. This provides interesting insight into the origin of the AB effect. Some clarifications are also made regarding the experimental verification of this effect.
We respond to the points raised in the preceding Comment [] on our recent work [], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.