J 2024

The dressing field method for diffeomorphisms: a relational framework

FRANCOIS, Jordan Thomas

Basic information

Original name

The dressing field method for diffeomorphisms: a relational framework

Authors

FRANCOIS, Jordan Thomas (250 France, guarantor, belonging to the institution)

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Impact factor

Impact factor: 2.100 in 2022

Organization unit

Faculty of Science

DOI

UT WoS

001269820800001

Keywords in English

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

Tags

Tags

International impact, Reviewed
Změněno: 7/8/2024 11:11, Mgr. Marie Šípková, DiS.

Abstract

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.

Links

EH22_010/0003229, research and development project
Name: MSCAfellow5_MUNI