Geometric Relational Framework for General-Relativistic Gauge Field Theories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00143737" target="_blank" >RIV/00216224:14310/25:00143737 - isvavai.cz</a>

Výsledek na webu

<a href="https://onlinelibrary.wiley.com/doi/10.1002/prop.202400149" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/prop.202400149</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/prop.202400149" target="_blank" >10.1002/prop.202400149</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Geometric Relational Framework for General-Relativistic Gauge Field Theories

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Geometric Relational Framework for General-Relativistic Gauge Field Theories

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10303 - Particles and field physics

Projekt

<a href="/cs/project/EH22_010%2F0003229" target="_blank" >EH22_010/0003229: MSCAfellow5_MUNI</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS

ISSN

0015-8208

e-ISSN

1521-3978

Svazek periodika

73

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

56

Strana od-do

1-56

Kód UT WoS článku

001354393800001

EID výsledku v databázi Scopus

2-s2.0-85208438303