J 2024

The dressing field method for diffeomorphisms: a relational framework

FRANCOIS, Jordan Thomas

Základní údaje

Originální název

The dressing field method for diffeomorphisms: a relational framework

Autoři

FRANCOIS, Jordan Thomas (250 Francie, garant, domácí)

Vydání

Journal of Physics A: Mathematical and Theoretical, IOP Publishing Ltd, 2024, 1751-8113

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Impakt faktor

Impact factor: 2.100 v roce 2022

Organizační jednotka

Přírodovědecká fakulta

DOI

UT WoS

001269820800001

Klíčová slova anglicky

relationality; bundle geometry; covariant phase space; gravitational dressings; edge modes

Štítky

Příznaky

Mezinárodní význam, Recenzováno
Změněno: 7. 8. 2024 11:11, Mgr. Marie Šípková, DiS.

Anotace

V originále

The dressing field method (DFM) is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M)-invariant objects, which has a natural relational interpretation. Its precise formulation relies on a clear understanding of the bundle geometry of field space. By detailing it, among other things we stress the geometric nature of field-independent and field-dependent diffeomorphisms, and highlight that the heuristic 'extended bracket' for field-dependent vector fields often featuring in the covariant phase space literature can be understood as arising from the Fr & ouml;licher-Nijenhuis bracket. Furthermore, by articulating this bundle geometry with the covariant phase space approach, we give a streamlined account of the elementary objects of the (pre)symplectic structure of a Diff(M)-theory: Noether charges and their bracket, as induced by the standard prescription for the presymplectic potential and 2-form. We give conceptually transparent expressions allowing to read the integrability conditions and the circumstances under which the bracket of charge is Lie, and the resulting Poisson algebras of charges are central extensions of the Lie algebras of field-independent (diff(M)) and field-dependent vector fields.We show that, applying the DFM, one obtains a Diff(M)-invariant and manifestly relational formulation of a general relativistic field theory. Relying on results just mentioned, we easily derive the 'dressed' (relational) presymplectic structure of the theory. This reproduces or extends results from the gravitational edge modes and gravitational dressings literature. In addition to simplified technical derivations, the conceptual clarity of the framework supplies several insights and allows us to dispel misconceptions.

Návaznosti

EH22_010/0003229, projekt VaV
Název: MSCAfellow5_MUNI