Geometric relational framework for general-relativistic gauge field theories
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910732191268864 |
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| author | François, Jordan Ravera, Lucrezia |
| author_facet | François, Jordan Ravera, Lucrezia |
| contents | We remind how relationality arises as the core insight of general-relativistic gauge field theories from the articulation of the generalised hole and point-coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. We propose our formulation for such a framework, based on a significant development of the dressing field method of symmetry reduction.
We first develop a version for the group $\text{Aut}(P)$ of automorphisms of a principal bundle $P$ over a manifold $M$, as it is the most natural and elegant, and as $P$ hosts all the mathematical structures relevant to general-relativistic gauge field theory. Yet, as the standard formulation is local, on $M$, we then develop the relational framework for local field theory. It manifestly implements the generalised point-coincidence argument, whereby the physical field-theoretical degrees of freedoms co-define each other and define, coordinatise, the physical spacetime itself. Applying the framework to General Relativity, we obtain relational Einstein equations, encompassing various notions of "scalar coordinatisation" à la Kretschmann-Komar and Brown-Kuchař. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric relational framework for general-relativistic gauge field theories François, Jordan Ravera, Lucrezia General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We remind how relationality arises as the core insight of general-relativistic gauge field theories from the articulation of the generalised hole and point-coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. We propose our formulation for such a framework, based on a significant development of the dressing field method of symmetry reduction. We first develop a version for the group $\text{Aut}(P)$ of automorphisms of a principal bundle $P$ over a manifold $M$, as it is the most natural and elegant, and as $P$ hosts all the mathematical structures relevant to general-relativistic gauge field theory. Yet, as the standard formulation is local, on $M$, we then develop the relational framework for local field theory. It manifestly implements the generalised point-coincidence argument, whereby the physical field-theoretical degrees of freedoms co-define each other and define, coordinatise, the physical spacetime itself. Applying the framework to General Relativity, we obtain relational Einstein equations, encompassing various notions of "scalar coordinatisation" à la Kretschmann-Komar and Brown-Kuchař. |
| title | Geometric relational framework for general-relativistic gauge field theories |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.04043 |