Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambigui...

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Detalhes bibliográficos
Autores: Ordóñez, C. R., Pons Ràfols, Josep Maria
Formato: artículo
Estado:Versión publicada
Fecha de publicación:1995
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/24569
Acesso em linha:https://hdl.handle.net/2445/24569
Access Level:acceso abierto
Palavra-chave:Teoria de grups
Camps de galga (Física)
Teoria quàntica
Group theory
Gauge fields (Physics)
Quantum theory
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spelling Dirac and reduced quantization: A Lagrangian approach and Application to Coset SpacesOrdóñez, C. R.Pons Ràfols, Josep MariaTeoria de grupsCamps de galga (Física)Teoria quànticaGroup theoryGauge fields (Physics)Quantum theoryA Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics.American Institute of Physics201220121995info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion20 p.application/pdfhttps://hdl.handle.net/2445/24569Articles publicats en revistes (Física Quàntica i Astrofísica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document proporcionada per AIP i http://dx.doi.org/10.1063/1.531111Journal of Mathematical Physics, 1995, vol. 1146http://dx.doi.org/10.1063/1.531111(c) American Institute of Physics, 1995info:eu-repo/semantics/openAccessoai:recercat.cat:2445/245692026-05-29T05:05:01Z
dc.title.none.fl_str_mv Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
title Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
spellingShingle Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
Ordóñez, C. R.
Teoria de grups
Camps de galga (Física)
Teoria quàntica
Group theory
Gauge fields (Physics)
Quantum theory
title_short Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
title_full Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
title_fullStr Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
title_full_unstemmed Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
title_sort Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces
dc.creator.none.fl_str_mv Ordóñez, C. R.
Pons Ràfols, Josep Maria
author Ordóñez, C. R.
author_facet Ordóñez, C. R.
Pons Ràfols, Josep Maria
author_role author
author2 Pons Ràfols, Josep Maria
author2_role author
dc.subject.none.fl_str_mv Teoria de grups
Camps de galga (Física)
Teoria quàntica
Group theory
Gauge fields (Physics)
Quantum theory
topic Teoria de grups
Camps de galga (Física)
Teoria quàntica
Group theory
Gauge fields (Physics)
Quantum theory
description A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics.
publishDate 1995
dc.date.none.fl_str_mv 1995
2012
2012
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/2445/24569
url https://hdl.handle.net/2445/24569
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document proporcionada per AIP i http://dx.doi.org/10.1063/1.531111
Journal of Mathematical Physics, 1995, vol. 1146
http://dx.doi.org/10.1063/1.531111
dc.rights.none.fl_str_mv (c) American Institute of Physics, 1995
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Institute of Physics, 1995
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 20 p.
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv Articles publicats en revistes (Física Quàntica i Astrofísica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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