Is the Aharonov-Bohm phase shift for a non-closed path a measurable
quantity ?
- URL: http://arxiv.org/abs/2305.15658v2
- Date: Tue, 30 Jan 2024 02:08:23 GMT
- Title: Is the Aharonov-Bohm phase shift for a non-closed path a measurable
quantity ?
- Authors: Masashi Wakamatsu
- Abstract summary: We show that the origin of the AB-phase can be traced back to other part of our effective Hamiltonian.
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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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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