March, Eleanor and Weatherall, James Owen (2024) A Puzzle About General Covariance and Gauge. [Preprint]

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Abstract

We consider two simple criteria for when a physical theory should be said to be “generally covariant”, and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is that the bundles encountered in Yang-Mills theory are not natural bundles; instead, they are gauge-natural. We then show how these observations relate to previous arguments about the significance of solder forms in assessing disanalogies between general relativity and Yang-Mills theory. We conclude by suggesting that general covariance is really about functoriality.

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Item Type:	Preprint
Creators:	Creators Email ORCID March, Eleanor eleanor.march@balliol.ox.ac.uk Weatherall, James Owen weatherj@uci.edu 0000-0003-1461-7821
Keywords:	general covariance, Yang-Mills theory, solder forms, general relativity, natural bundles
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	James Owen Weatherall
Date Deposited:	07 May 2024 10:44
Last Modified:	07 May 2024 10:44
Item ID:	23381
Subjects:	Specific Sciences > Physics Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	2024
URI:	https://philsci-archive.pitt.edu/id/eprint/23381

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