Why Gauge? Conceptual Aspects of Gauge Theory

This thesis is about conceptual aspects of gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the standard model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question the thesis aims to answer is: how can descriptive redundancy be fruitful for physics? This question embraces many important topics in the philosophical literature on gauge theory, which I will address. This thesis has two main Parts. Part \ref{part:I} provides technical and conceptual background. It relates the redundancies of gauge theories with the redundancies in the foundations of spacetime physics. In particular, to those of Einstein's theory of general relativity, that are more familar to the average philosopher. This Part provides a perspicuous, geometrical understanding of the physics of gauge theory, on a par with the chronogeometric understanding of general relativity. In Part II I will assess two surprising uses of and one contentious question about gauge symmetry. First, I will provide one answer to the question: ``Why gauge theory?'', that is: why introduce redundancies in our models of nature in the first place? This type of answer is pragmatic: because such redundancies are useful for model-building, in a particular way; and they allow us to focus our mathematical apparatus on different aspects of the same phenomena. Second, I present a choice of gauge that is related to a physically natural, and general, splitting of the electric field; which undermines the way one usually thinks of a choice of gauge as motivated by calculational convenience, or as completely arbitrary. Last, I will assess arguments and counter-arguments for the direct physical significance of gauge symmetries. The conclusion provides a second type of answer to the question of ``Why gauge?''. Namely: because we need it to couple subsystems.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2022

Author dc:creator

• Gomes, Henrique

Advisor dc:contributor.advisor

• Butterfield, Jeremy

• Gauge theory
• Gravity
• spacetime
• symmetry

Licence

• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.86554

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/339145