Borsboom, Silvester (2024) Spontaneous Breaking of Global Gauge Symmetries in the Higgs Mechanism. UNSPECIFIED.

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Abstract

The Higgs mechanism is invoked to explain how gauge bosons can be massive while Yang-Mills theory describes only massless gauge fields. Central to it is the notion of spontaneous symmetry breaking (SSB), applied to the SU(2) × U(1) gauge symmetry of the electroweak theory. However, over the past two decades, philosophers of physics have challenged the standard narrative of the Higgs mechanism as an instance of gauge symmetry breaking. They have pointed out the apparent contradiction between the status of gauge symmetries as mathematical redundancies and the account of mass generation in the Higgs mechanism by means of gauge symmetry breaking. In addition, they have pointed to Elitzur's theorem, a result from lattice gauge theory forbidding local gauge symmetry breaking. This has led philosophers to the conclusion that there cannot be any SSB in the Higgs mechanism, an idea supported by the dressing field method of gauge symmetry reduction. In this thesis we mitigate this conclusion by showing that global gauge symmetries, i.e. transformations independent of spacetime, are not mere mathematical redundancies but carry direct empirical significance. This can be seen from constrained Hamiltonian analysis by the fact that the Gauss constraint in Yang-Mills theory only generates gauge transformations which asymptotically become the identity. The classical Higgs mechanism can indeed be reformulated as a breaking of only this global gauge symmetry. We subsequently extend this result to quantum field theory by considering SSB in algebraic quantum field theory (AQFT). The Abelian U(1) Higgs mechanism can be shown to be an instance of SSB in the algebraic sense and we discuss the extent to which this can be generalised to the non-Abelian case. Finally we discuss the implications of our results for the interpretation of the electroweak phase transition and the analogy between the Higgs mechanism and superconductivity.

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Item Type:	Other
Creators:	Creators Email ORCID Borsboom, Silvester silvester.borsboom@ru.nl 0009-0006-0602-9789
Additional Information:	Double master thesis for MSc Mathematics and MSc Physics & Astronomy at University of Amsterdam, under supervision of Sebastian de Haro and Hessel Posthuma. Won two prizes, one of which was the Hanneke Jansen memorial prize for history and philosophy of physics.
Keywords:	gauge theory, Higgs mechanism, spontaneous symmetry breaking, quantum field theory, philosophy of physics, gauge symmetry, gauge invariance, global, gauge, Higgs, symmetry, symmetry breaking, quantum, AQFT, algebraic quantum field theory
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Condensed Matter Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Mr. Silvester Borsboom
Date Deposited:	17 Dec 2024 13:12
Last Modified:	17 Dec 2024 13:12
Item ID:	24403
Official URL:	https://scripties.uba.uva.nl/search?id=record_5459...
DOI or Unique Handle:	10.13140/rg.2.2.31890.88009
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Condensed Matter Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Symmetries/Invariances
Date:	4 July 2024
URI:	https://philsci-archive.pitt.edu/id/eprint/24403

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