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

TL;DR

This paper critically reevaluates the classical limit of the Aharonov-Bohm effect, arguing that it has no classical analog and emphasizing the physical reality of electromagnetic potentials through a topological approach and phase factors.

Contribution

It provides a critique of Feynman's classical limit arguments, introduces the Fock-London-Weyl phase factor, and proposes a topological framework linking the AB effect to modular angular momentum exchange.

Findings

Feynman's arguments on classical limits are physically untenable.

The AB effect has no classical analog, supporting the view of electromagnetic potentials as physically real.

A topological approach highlights the role of interaction field momentum and modular angular momentum.

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.