Gomes, Henrique (2022) Same-Diff? Conceptual similarities between gauge transformations and diffeomorphisms Part I: Symmetries and isomorphisms. [Preprint]

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Abstract

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in which are they different? To what extent are we justified in endorsing different attitudes---nowadays called sophistication, haecceitism, and eliminativism---towards each? This is the first of four papers taking up this question.

This first paper will discuss notions of symmetries and isomorphisms that will be used in the remaining papers in the series. There are several such notions in the literature and the question of how they mesh with empirical discernibility is a delicate one; even the orthodox view that symmetries are empirically unobservable (even in principle) has recently been challenged by \cite{Belot_sym}. Focusing on local field theories, I will provide a precise definition of dynamical symmetries in terms of the space of states of the theory at hand. I will then apply the definition to Yang-Mills theories and general relativity and show that these symmetries correspond to automorphisms of `natural' geometric structures: the small diffeomorphisms of the spacetime manifold and the small fiber-preserving diffeomorphisms of a fibered space. Finally, I will show that these automorphisms can be given a passive gloss, since they correspond 1-1 to the coordinate transformations of the underlying manifolds.

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Item Type:	Preprint
Creators:	Creators Email ORCID Gomes, Henrique gomes.ha@gmail.com 0000-0002-9285-0090
Keywords:	Symmetries, diffeomorphisms, gauge, hole argument, Yang-Mills, isomorphisms.
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Dr Henrique Gomes
Date Deposited:	25 Oct 2022 17:23
Last Modified:	25 Oct 2022 17:23
Item ID:	21309
Subjects:	Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	2022
URI:	https://philsci-archive.pitt.edu/id/eprint/21309

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