Physical reality of electromagnetic potentials and the classical limit of the Aharonov-Bohm effect

Abstract

Recent literature on the Aharonov-Bohm effect has raised fundamental questions on the classical correspondence of this effect and the physical reality of the electromagnetic potentials in quantum mechanics. Reappraisal on Feynman's approach to the classical limit of AB effect is presented. The critique throws light on the significance of quantum interference and quantum phase shifts in any such classical correspondence. Detailed analysis shows that Feynman arguments are untenable on physical grounds and the claim made in the original AB paper that this effect had no classical analog seems valid. The importance of nonintegrable phase factor distinct from the AB phase factor, here termed as Fock-London-Weyl phase factor for the historical reasons, is underlined in connection with the classical aspects/limits. A topological approach incorporating the physical significance of the interaction field momentum is proposed. A new idea emerges from this approach that attributes the origin of the AB effect to the exchange of modular angular momentum.

Section III revised, 10 pages, 4 figures, Quantum Studies: Mathematics and Foundations Online published 11 August, 2017

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• Coulomb- quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex
• Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics
• Magnetic forces in the absence of a classical magnetic field
• Symmetry of Dirac two-oscillator system, gauge-invariance, and Landau problem