Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the origi...

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Detalhes bibliográficos
Autores: Pons Ràfols, Josep Maria, Salisbury, D. C., Shepley, L. C.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:1997
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/12425
Acesso em linha:https://hdl.handle.net/2445/12425
Access Level:acceso abierto
Palavra-chave:Relativitat (Física)
Càlcul de variacions
Gravitació
Relativity (Physics)
Calculus of variations
Gravitation
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spelling Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theoriesPons Ràfols, Josep MariaSalisbury, D. C.Shepley, L. C.Relativitat (Física)Càlcul de variacionsGravitacióRelativity (Physics)Calculus of variationsGravitationWe study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.The American Physical Society1997info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/12425Articles publicats en revistes (Física Quàntica i Astrofísica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció digital del document publicat en format paper, proporcionada per PROLA i http://dx.doi.org/10.1103/PhysRevD.55.658Physical Review D, 1997, vol. 55, núm. 2, p. 658-668http://dx.doi.org/10.1103/PhysRevD.55.658(c) The American Physical Society, 1997info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/124252026-05-27T06:46:51Z
dc.title.none.fl_str_mv Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
title Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
spellingShingle Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
Pons Ràfols, Josep Maria
Relativitat (Física)
Càlcul de variacions
Gravitació
Relativity (Physics)
Calculus of variations
Gravitation
title_short Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
title_full Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
title_fullStr Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
title_full_unstemmed Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
title_sort Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories
dc.creator.none.fl_str_mv Pons Ràfols, Josep Maria
Salisbury, D. C.
Shepley, L. C.
author Pons Ràfols, Josep Maria
author_facet Pons Ràfols, Josep Maria
Salisbury, D. C.
Shepley, L. C.
author_role author
author2 Salisbury, D. C.
Shepley, L. C.
author2_role author
author
dc.subject.none.fl_str_mv Relativitat (Física)
Càlcul de variacions
Gravitació
Relativity (Physics)
Calculus of variations
Gravitation
topic Relativitat (Física)
Càlcul de variacions
Gravitació
Relativity (Physics)
Calculus of variations
Gravitation
description We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.
publishDate 1997
dc.date.none.fl_str_mv 1997
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/12425
url https://hdl.handle.net/2445/12425
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció digital del document publicat en format paper, proporcionada per PROLA i http://dx.doi.org/10.1103/PhysRevD.55.658
Physical Review D, 1997, vol. 55, núm. 2, p. 658-668
http://dx.doi.org/10.1103/PhysRevD.55.658
dc.rights.none.fl_str_mv (c) The American Physical Society, 1997
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) The American Physical Society, 1997
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv The American Physical Society
publisher.none.fl_str_mv The American Physical Society
dc.source.none.fl_str_mv Articles publicats en revistes (Física Quàntica i Astrofísica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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