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WORLD SCIENTIFIC (EUROPE) eBooks

The Aharonov–Bohm Effect, Proca Fields, and Flux Quantization

Giorgio Vassallo, Antonino Oscar Di Tommaso

Published Jul 1, 2022• 0 citations
Publisher
DOI
10.1142/9781800611306_0004

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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.
The Aharonov-Bohm (AB) effect was tested under conditions where an electron wave and a magnetic field did not overlap: the Meissner effect of the superconductor shielding a toroidal ferromagnet eliminated the leakage field. Using the newly-developed technique of electron holography, conclusive evidence for the AB effect was obtained by detecting a relative phase shift of π between the two electron waves passing through the hole and outside the toroid. The detected phase shift value of exactly π comes from the quantization of the magnetic flux within the superconductor. This quantization assures the complete shielding of the magnetic field.