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Is the world made of loops?

Afriat, Alexander (2018) Is the world made of loops? [Preprint]

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Abstract

I see no good reason to prefer (any version I know of) the `holonomy interpretation' to the `potential interpretation' of the Aharonov-Bohm effect. Everyone agrees that the inverse image $[A]=[A+d\lambda]_{\lambda}=d^{-1}F$ of the electromagnetic field $F$ is a class, full of individuals; and that the circulation $\small{\textsf{C}}$ of the electromagnetic potential $A$ around a loop $\sigma_0$ encircling the solenoid is common to the whole class $[A]$, and to the homotopy class or \emph{hoop} $[\sigma_0]$. If picking individuals out of classes is the problem, picking an individual potential out of $[A]$ should be no worse than picking an individual loop out of $[\sigma_0]$. The individuals of $[A]$ can moreover be transcended---punctually, without integration around loops---by an appropriate version of the electromagnetic connection.

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Item Type: Preprint
Creators:
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Afriat, Alexanderafriat@gmail.com
Keywords: gauge, loops, potentials, holonomy interpretation, Aharonov-Bohm
Subjects: Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Alexander Afriat
Date Deposited: 08 Sep 2018 16:08
Last Modified: 08 Sep 2018 16:08
Item ID: 15012
Subjects: Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Symmetries/Invariances
Date: 7 September 2018
URI: https://philsci-archive.pitt.edu/id/eprint/15012

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