Gomes, Henrique (2025) The Aharonov-Bohm effect: reality and folklore. [Preprint]

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Abstract

The Aharonov-Bohm (A-B) effect has been a major focus of the foundations of physics. And yet, much confusion persists. In particular, the effect purportedly leads to a dilemma: on one horn, we have a non-local action of a gauge-invariant quantity on charged particles; on the other, we get a local action on these particles, but of a non-gauge invariant quantity. This is the folklore, but the folklore is filled with misconceptions. Here, by deploying a recently defended formulation of gauge theory that dispenses with principal bundles, gauge potentials, and explicit gauge symmetries, I argue, with previous authors, that the A-B effect can be understood gauge-independently. But here my argument will go further: I will show that the A-B effect, when expressed in terms of the covariant derivative of a vector bundle, is \emph{entirely} analogous to the holonomy of \emph{spacetime} vectors, and can be understood completely locally. The only surprising idea illustrated by the A-B effect is that, in some circumstances, there is more to the covariant derivative than can be accounted for by the curvature and underlying topology of a vector bundle.

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Item Type:	Preprint
Creators:	Creators Email ORCID Gomes, Henrique gomes.ha@gmail.com 0000-0002-9285-0090
Keywords:	Aharonov-Bohm effect, non-locality, gauge theory, general relativity.
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Dr Henrique Gomes
Date Deposited:	24 Sep 2025 11:12
Last Modified:	24 Sep 2025 11:12
Item ID:	26727
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Symmetries/Invariances
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26727

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