Geometric Relational Framework for General-Relativistic Gauge Field Theories
| Autoři | |
|---|---|
| Rok publikování | 2025 |
| Druh | Recenzovaný odborný článek |
| Časopis / Zdroj | FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://onlinelibrary.wiley.com/doi/10.1002/prop.202400149 |
| Doi | https://doi.org/10.1002/prop.202400149 |
| Klíčová slova | General-relativistic gauge theories; Relationality; Bundle geometry; Field space; Relational Einstein equations; Scalar coordinatisation |
| Přiložené soubory | |
| Popis | 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 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” `a la Kretschmann-Komar and Brown-Kuchaˇr. |
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