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 in the presence of boundary conditions. The symmetry that is spontaneously broken by the Higgs mechanism is this global one. Second, we explain how the Coulomb gauge is the preferred gauge for a gauge-invariant account of the Abelian Higgs mechanism. Based on the existence of the physical global gauge symmetry, 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:	18 Nov 2025 13:51
Last Modified:	18 Nov 2025 13:51
Item ID:	27242
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/27242

Available Versions of this Item

• Global Gauge Symmetry Breaking in the Abelian Higgs Mechanism. (deposited 24 Apr 2025 13:11)
  • Global Gauge Symmetry Breaking in the Abelian Higgs Mechanism. (deposited 18 Nov 2025 13:51) [Currently Displayed]

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