A Puzzle About General Covariance and Gauge
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915195608104960 |
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| author | March, Eleanor Weatherall, James Owen |
| author_facet | March, Eleanor Weatherall, James Owen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Puzzle About General Covariance and Gauge March, Eleanor Weatherall, James Owen History and Philosophy of Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | A Puzzle About General Covariance and Gauge |
| topic | History and Philosophy of Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.03906 |