Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Aharonov-Bohm effect and the mass of the photon

David G. Boulware, S. Deser

Published Nov 1, 1989• 29 citations
Publisher

Abstract

We show that the Aharonov-Bohm effect requires that the vector potential couple minimally to matter, not that it be a gauge field: The effect is present in massive (finite-range) electrodynamics, reducing smoothly to the original result in the limit of infinite range. Indeed, it may be used to provide an experimental bound on the range which is much larger than the ``table-top'' apparatus, namely a lower limit of order ${10}^{2}$ km.

DOI
10.1103/physrevlett.63.2319

Related papers

Aharonov-Bohm effect in Generalized Electrodynamics

C. A. M. de Melo, Bruno Peres, J C Sumire Esquia +1 more

The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally U(1)-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.

arXiv:2407.05501•Nuclear Physics B•Jul 6, 2024•1 citation

Deflating the Aharonov-Bohm Effect

David Wallace

I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics (or at least, to an account no more nonlocal than quantum theory in general requires); I sketch a possible such account.

arXiv:1407.5073•Jul 18, 2014•11 citations

Experimental confirmation of the aharonov-bohm effect

Tonomura

Experimental evidence was obtained for the existence of the AB effect. This effect has been a subject of long controversy regarding the physical significance of gauge fields, -- in the present case, the vector potentials.

Conference on Precision Electromagnetic Measurements•Jan 1, 1988•1 citation

Aharonov-Bohm effect mediated by massive photons

Kicheon Kang

Abstract Virtual photons play an essential role in the locally realistic description of the Aharonov-Bohm interference. We show that the effect of virtual photons in the interferometer is manifested by a change in their spectrum. In particular, when a vacuum is confined between two ideal conducting plates, the photons obey the two-dimensional Proca equation, the wave equation with finite effective mass. This results in a short-range interaction between a test charge and a magnetic flux, and hence the Aharonov-Bohm effect is reduced exponentially at a large distance between the two bodies. On the other hand, a semiclassical description is also possible, and this raises the interesting question of how to prove the physical reality of virtual photons.

arXiv:2403.03495•Europhysics Letters (EPL)•Sep 1, 2024•2 citations

Gauge invariance of the Aharonov-Bohm effect

M. Babiker, R. Loudon

It is argued that much of the recent controversy over the Aharonov-Bohm effect has been fuelled by the widespread consideration of solenoids of infinite length: in this limit, the field and the vector potential have somewhat anomalous properties and it appears superficially that the Aharonov-Bohm phase shift can be changed by a gauge transformation. This incorrect impression is here removed by considering a solenoid of finite length and by carefully distinguishing the longitudinal and transverse parts of the vector potential. It is shown that the phase shift depends only on the transverse part of the vector potential and it cannot be changed by a gauge transformation. The nature of the difficulty that occurs in the limit of a solenoid of infinite length is examined in detail. The finite-length theory given here also provides guidelines for the design of experiments on the Aharonov-Bohm effect.

Journal of Physics A Mathematical and General•Oct 21, 1984•16 citations

Some aspects of the Aharonov-Bohm effect

Walter C. Henneberger

It is shown that the Aharonov-Bohm scattering cross section diverges. This presents a problem since the range of the scattering force (Lorentz force) is finite. The cross section found by Aharonov and Bohm (AB) results whether one takes an incident wave function corresponding to particles moving in the incident direction, as was done by AB, or just takes the incident state to be a plane wave. The mechanism by which a localized force results in an infinite cross section is not clear. This is an apparent contradiction to recent proofs that electrodynamics is a local theory.

Physical Review A•Oct 1, 1980•38 citations
We show that the Aharonov-Bohm effect requires that the vector potential couple minimally to matter, not that it be a gauge field: The effect is present in massive (finite-range) electrodynamics, reducing smoothly to the original result in the limit of infinite range. Indeed, it may be used to provide an experimental bound on the range which is much larger than the ``table-top'' apparatus, namely a lower limit of order 102{10}^{2}102 km.
The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally U(1)-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.
I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics (or at least, to an account no more nonlocal than quantum theory in general requires); I sketch a possible such account.
Abstract Virtual photons play an essential role in the locally realistic description of the Aharonov-Bohm interference. We show that the effect of virtual photons in the interferometer is manifested by a change in their spectrum. In particular, when a vacuum is confined between two ideal conducting plates, the photons obey the two-dimensional Proca equation, the wave equation with finite effective mass. This results in a short-range interaction between a test charge and a magnetic flux, and hence the Aharonov-Bohm effect is reduced exponentially at a large distance between the two bodies. On the other hand, a semiclassical description is also possible, and this raises the interesting question of how to prove the physical reality of virtual photons.
It is argued that much of the recent controversy over the Aharonov-Bohm effect has been fuelled by the widespread consideration of solenoids of infinite length: in this limit, the field and the vector potential have somewhat anomalous properties and it appears superficially that the Aharonov-Bohm phase shift can be changed by a gauge transformation. This incorrect impression is here removed by considering a solenoid of finite length and by carefully distinguishing the longitudinal and transverse parts of the vector potential. It is shown that the phase shift depends only on the transverse part of the vector potential and it cannot be changed by a gauge transformation. The nature of the difficulty that occurs in the limit of a solenoid of infinite length is examined in detail. The finite-length theory given here also provides guidelines for the design of experiments on the Aharonov-Bohm effect.
It is shown that the Aharonov-Bohm scattering cross section diverges. This presents a problem since the range of the scattering force (Lorentz force) is finite. The cross section found by Aharonov and Bohm (AB) results whether one takes an incident wave function corresponding to particles moving in the incident direction, as was done by AB, or just takes the incident state to be a plane wave. The mechanism by which a localized force results in an infinite cross section is not clear. This is an apparent contradiction to recent proofs that electrodynamics is a local theory.