Local description of the Aharonov-Bohm effect with a quantum electromagnetic field

Abstract

In the seminal works from Santos and Gozalo [Europhys. Lett. $45$, 418 (1999)] and Marletto and Vedral [Phys. Rev. Lett. $125$, 040401 (2020)], it is shown how the Aharonov-Bohm effect can be described as the result of an exchange of virtual photons between the solenoid and the quantum charged particle along its propagation through the interferometer, where both the particle and the solenoid interact locally with the quantum electromagnetic field. This interaction results in a local and gauge-independent phase generation for the particle propagation in each path of the interferometer. Here we improve the cited treatments by using the quantum electrodynamics formalism in the Lorentz gauge, with a manifestly gauge-independent Hamiltonian for the interaction and the presence of virtual longitudinal photons. Only with this more complete and gauge-independent treatment it is possible to justify the acquired phases for interferometers with arbitrary geometries, and this is an advantage of our treatment. We also extend the results to the electric version of the Aharonov-Bohm effect. Finally, we propose an experiment that could test the locality of the Aharonov-Bohm phase generation.

6 pages, 3 figures. v4: Minor changes in the text

References in corpus (2)

• A macroscopic test of the Aharonov-Bohm effect
• The Aharonov-Bohm phase is locally generated (like all other quantum phases)

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• Gauge invariance of the local phase in the Aharonov-Bohm interference: quantum electrodynamic approach
• The Aharonov-Bohm effect in a closed flux line
• Gauge invariance of the Aharonov-Bohm effect in a quantum electrodynamics framework
• Aharonov-Bohm effect mediated by massive photons
• Topological schemes in spacetime for the electrodynamic Aharonov-Bohm effect
• Gauge dependence of the Aharonov-Bohm phase in a quantum electrodynamics framework
• Topology of the Aharonov-Bohm effect in different reference frames