The dressing field method for diffeomorphisms: a relational framework
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00136712" target="_blank" >RIV/00216224:14310/24:00136712 - isvavai.cz</a>
Result on the web
<a href="https://iopscience.iop.org/article/10.1088/1751-8121/ad5cad" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/ad5cad</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ad5cad" target="_blank" >10.1088/1751-8121/ad5cad</a>
Alternative languages
Result language
angličtina
Original language name
The dressing field method for diffeomorphisms: a relational framework
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EH22_010%2F0003229" target="_blank" >EH22_010/0003229: MSCAfellow5_MUNI</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A: Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
1751-8121
Volume of the periodical
57
Issue of the periodical within the volume
30
Country of publishing house
GB - UNITED KINGDOM
Number of pages
84
Pages from-to
1-84
UT code for WoS article
001269820800001
EID of the result in the Scopus database
2-s2.0-85198730096