https://doi.org/10.1140/epjp/s13360-024-04922-9
Regular Article
Is the Aharonov–Bohm phase shift for a non-closed path a measurable quantity?
KEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Oho 1-1, 305-0801, Tsukuba, Ibaraki, Japan
Received:
21
July
2023
Accepted:
19
January
2024
Published online:
1
February
2024
There recently appear some interesting attempts to explain the AB-effect through the interaction between the charged particle and the solenoid current mediated by the exchange of a virtual photon. A vital assumption of this approach is that AB-phase shift is proportional to the change of the interaction energy between the charged particle and solenoid along the path of the moving charge. Accordingly, they insist that the AB-phase change along a path does not depend on the gauge choice so that the AB-phase shift for a non-closed path is in principle measurable. We however notice the existence of two fairly different discussions on the interaction energy between the solenoid and a charge particle, the one is due to Boyer and the other is due to Saldanha and others. In the present paper, based on a self-contained quantum mechanical treatment of the combined system of a solenoid, a charged particle, and the quantized electromagnetic fields, we show that both interaction energies of Boyer and of Saldanha are in fact gauge invariant at least for non-singular gauge transformations but they are destined to cancel each other. Our analysis rather shows that the origin of the AB-phase can be traced back to other part of our effective Hamiltonian. Furthermore, based on the path-integral formalism with our effective Lagrangian, we explicitly demonstrate that the AB-phase shift for a non-closed path is not a gauge-variant quantity, which means that it would not correspond to direct experimental observables.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.