Borsboom, Silvester and De Haro, Sebastian (2025) Global Gauge Symmetry Breaking in the Abelian Higgs Mechanism. [Preprint]

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Abstract

This paper aims to resolve the incompatibility between two extant gauge-invariant accounts of the Abelian Higgs mechanism: the first account uses global gauge symmetry breaking, and the second eliminates spontaneous symmetry breaking entirely. We resolve this incompatibility by using the constrained Hamiltonian formalism in symplectic geometry. First we argue that, unlike their local counterparts, global gauge symmetries are physical. The symmetries that are spontaneously broken by the Higgs mechanism are then the global ones. Second, we explain how the dressing field method singles out the Coulomb gauge as a preferred gauge for a gauge-invariant account of the Abelian Higgs mechanism. Based on the existence of this group of global gauge symmetries that are physical, we resolve the incompatibility between the two accounts by arguing that the correct way to carry out the second method is to eliminate only the redundant gauge symmetries, i.e. those local gauge symmetries which are not global. We extend our analysis to quantum field theory, where we show that the Abelian Higgs mechanism can be understood as spontaneous global U(1) symmetry breaking in the C*-algebraic sense.

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Item Type:	Preprint
Creators:	Creators Email ORCID Borsboom, Silvester silvester.borsboom@ru.nl 0009-0006-0602-9789 De Haro, Sebastian s.deharo@uva.nl 0000-0002-3000-5967
Keywords:	Higgs mechanism, gauge symmetry, symmetry breaking, quantum field theory, classical field theory
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Mr. Silvester Borsboom
Date Deposited:	24 Apr 2025 13:11
Last Modified:	24 Apr 2025 13:11
Item ID:	25158
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	24 April 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25158

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