Gao, Shan (2025) Can Unitary Gauge Provide a Local and Gauge-Invariant Explanation of the Aharonov-Bohm Effect? [Preprint]
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Abstract
How to explain the Aharonov-Bohm (AB) effect remains deeply controversial, particularly regarding the tension between locality and gauge invariance. Recently Wallace argued that the AB effect can be explained in a local and gauge-invariant way by using the unitary gauge. In this paper, I present a critical analysis of Wallace's intriguing argument. First, I show that the unitary gauge transforms the Schroedinger equation into the Madelung equations, which are expressed entirely in terms of local and gauge-invariant quantities. Next, I point out that an additional quantization condition needs to be imposed in order that the Madelung equations are equivalent to the Schroedinger equation, while the quantization condition is inherently nonlocal. Finally, I argue that the Madelung equations with the quantization condition can hardly explain the the AB effect, even if in a nonlocal way. This analysis suggests that the unitary gauge does not resolve the tension between locality and gauge invariance in explaining the AB effect, but highlights again the profound conceptual challenges in reconciling the AB effect with a local and gauge-invariant framework.
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| Item Type: | Preprint | ||||||
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| Keywords: | quantum mechanics; Aharonov-Bohm effect; locality; gauge invariance; unitary gauge; Madelung equations; quantization condition | ||||||
| Subjects: | Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Prof. Shan Gao | ||||||
| Date Deposited: | 04 Feb 2025 15:42 | ||||||
| Last Modified: | 04 Feb 2025 15:42 | ||||||
| Item ID: | 24678 | ||||||
| Subjects: | Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 4 February 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/24678 |
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