Gao, Shan (2026) Is the Electron Dressed? The Aharonov-Bohm Effect Challenges Dirac's Proposal. [Preprint]

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Abstract

The dressing field method (DFM), introduced by Dirac in 1955, constructs gauge-invariant matter fields by attaching a Wilson line to the bare field. This dressed field is often interpreted as the physical electron. In this paper we provide a rigorous analysis of Dirac's DFM. We begin by defining the dressed field and the associated dressed electromagnetic potential, and we examine their path-dependence and multi-valuedness in multiply-connected spaces. We then derive the exact Dirac equation satisfied by the dressed field, as well as its non-relativistic limit, the Schrödinger equation. The probabilistic interpretation (Born rule) is stated in terms of the dressed field. Next, we apply the theory to the Aharonov-Bohm (AB) effect. Using explicit computations, we show that the interference pattern predicted by the dressed field is independent of the magnetic flux \(\Phi\), in direct contradiction with the experimentally observed AB phase shift \(e^{-ie\Phi}\). We trace the mathematical origin of this failure to the exact cancellation of topological phases between the dressing factor and the bare wave function, which follows from Stokes' theorem and the multi-valuedness of the Wilson line in a multiply-connected space. Finally, we discuss the implications: the dressed field cannot serve as a complete physical description of the electron. The Dirac DFM is therefore not equivalent to standard quantum mechanics in topologically non-trivial backgrounds.

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Item Type:	Preprint
Creators:	Creators Email ORCID Gao, Shan sgao7319@uni.sydney.edu.au
Keywords:	dressing field method; Aharonov-Bohm effect; bare wave function; dressed field; multiply-connected space; holonomy
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Prof. Shan Gao
Date Deposited:	12 May 2026 14:53
Last Modified:	12 May 2026 14:53
Item ID:	29585
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances
Date:	12 May 2026
URI:	https://philsci-archive.pitt.edu/id/eprint/29585

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