Research Article

Comments on the Aharonov-Bohm Effect

Kazuyasu Shigemoto
Tezukayama University, Japan.
* Corresponding author
Kunihiko Uehara
Tezukayama University, Japan.
DOI icon 10.24018/ejphysics.2022.4.5.209

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Submitted 2022-09-04
Published 2022-10-20

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Article Main Content

In the original setting of the Aharonov-Bohm, the gauge invariant physical longitudinal mode of the vector potential, which is expressed by the gauge invariant physical current, gives the desired contribution to the Aharonov-Bohm effect. While the scalar mode of the vector potential, which changes under the gauge transformation so that it is the unphysical mode, give no contribution to the Aharonov-Bohm effect. Then Aharonov-Bohm effect really occurs by the physical longitudinal mode in the original Aharonov-Bohm’s setting. In the setting of Tonomura et al., where the magnet is shielded with the superconducting material, not only the magnetic field but also the longitudinal mode of the vector potential become massive by the Meissner effect. Then not only the magnetic field but also the physical longitudinal mode does not come out to the region where the electron travels. In such setting, only the scalar mode of the vector potential exists in the region where the electron travels, but there is no contribution to the Aharonov-Bohm effect from that mode.

Keywords: Aharonov-Bohm effect, non-simply connected region, physical longitudinal mode, Stokes’ theorem

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