What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910968450121728 |
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| author | Berghofer, Philipp François, Jordan Ravera, Lucrezia |
| author_facet | Berghofer, Philipp François, Jordan Ravera, Lucrezia |
| contents | On a mathematically foundational level, our most successful physical theories (gauge field theories and general-relativistic theories) are formulated in a framework based on the differential geometry of connections on principal bundles. After reviewing the essentials of this framework, we articulate the generalized hole and point-coincidence arguments, examining how they weight on a substantivalist position towards bundle spaces. This question, then, is considered in light of the Dressing Field Method, which allows a manifestly invariant reformulation of gauge field theories and general-relativistic theories, making their conceptual structure more transparent: it formally implements the point-coincidence argument and thus allows to define (dressed) fields and (dressed) bundle spaces immune to hole-type arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers Berghofer, Philipp François, Jordan Ravera, Lucrezia History and Philosophy of Physics General Relativity and Quantum Cosmology High Energy Physics - Theory On a mathematically foundational level, our most successful physical theories (gauge field theories and general-relativistic theories) are formulated in a framework based on the differential geometry of connections on principal bundles. After reviewing the essentials of this framework, we articulate the generalized hole and point-coincidence arguments, examining how they weight on a substantivalist position towards bundle spaces. This question, then, is considered in light of the Dressing Field Method, which allows a manifestly invariant reformulation of gauge field theories and general-relativistic theories, making their conceptual structure more transparent: it formally implements the point-coincidence argument and thus allows to define (dressed) fields and (dressed) bundle spaces immune to hole-type arguments. |
| title | What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers |
| topic | History and Philosophy of Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.12876 |