The dressing field method for diffeomorphisms: a relational
framework

FRANCOIS, Jordan Thomas. The dressing field method for diffeomorphisms: a relational framework. Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd, 2024, vol. 57, No 30, p. 1-84. ISSN 1751-8113. Available from: https://dx.doi.org/10.1088/1751-8121/ad5cad.

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TY  - JOUR
ID  - 2421888
AU  - Francois, Jordan Thomas
PY  - 2024
TI  - The dressing field method for diffeomorphisms: a relational framework
JF  - Journal of Physics A: Mathematical and Theoretical
VL  - 57
IS  - 30
SP  - 1-84
EP  - 1-84
PB  - IOP Publishing Ltd
SN  - 17518113
KW  - relationality
KW  - bundle geometry
KW  - covariant phase space
KW  - gravitational dressings
KW  - edge modes
UR  - https://iopscience.iop.org/article/10.1088/1751-8121/ad5cad
N2  - 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.
ER  -

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
Original language	English
Type of outcome	Article in a journal
Field of Study	10101 Pure mathematics
Country of publisher	United Kingdom of Great Britain and Northern Ireland
Confidentiality degree	is not subject to a state or trade secret
WWW	URL
Impact factor	Impact factor: 2.100 in 2022
Organization unit	Faculty of Science
Doi	http://dx.doi.org/10.1088/1751-8121/ad5cad
UT WoS	001269820800001
Keywords in English	relationality; bundle geometry; covariant phase space; gravitational dressings; edge modes
Tags	rivok
Tags	International impact, Reviewed
Changed by	Changed by: Mgr. Marie Šípková, DiS., učo 437722. Changed: 7/8/2024 11:11.

Abstract

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

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The dressing field method for diffeomorphisms: a relational framework

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