Some basics of su(1,1)

Detalhes bibliográficos
Autor(a) principal: Novaes,Marcel
Data de Publicação: 2004
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008
Resumo: A basic introduction to the su(1,1) algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, we rather emphasize the existing connections between them. We discuss two parametrizations of the coherent states manifold SU(1,1)/U(1): as the Poincaré disk in the complex plane and as the pseudosphere (a sphere in a Minkowskian space), and show that it is a natural phase space for quantum systems with SU(1,1) symmetry.
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spelling Some basics of su(1,1)su(1,1) algebraSU(1,1) groupcanonical transformationscoherent statessecond quantizationpseudosphereA basic introduction to the su(1,1) algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, we rather emphasize the existing connections between them. We discuss two parametrizations of the coherent states manifold SU(1,1)/U(1): as the Poincaré disk in the complex plane and as the pseudosphere (a sphere in a Minkowskian space), and show that it is a natural phase space for quantum systems with SU(1,1) symmetry.Sociedade Brasileira de Física2004-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008Revista Brasileira de Ensino de Física v.26 n.4 2004reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S1806-11172004000400008info:eu-repo/semantics/openAccessNovaes,Marceleng2005-04-20T00:00:00Zoai:scielo:S1806-11172004000400008Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2005-04-20T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Some basics of su(1,1)
title Some basics of su(1,1)
spellingShingle Some basics of su(1,1)
Novaes,Marcel
su(1,1) algebra
SU(1,1) group
canonical transformations
coherent states
second quantization
pseudosphere
title_short Some basics of su(1,1)
title_full Some basics of su(1,1)
title_fullStr Some basics of su(1,1)
title_full_unstemmed Some basics of su(1,1)
title_sort Some basics of su(1,1)
author Novaes,Marcel
author_facet Novaes,Marcel
author_role author
dc.contributor.author.fl_str_mv Novaes,Marcel
dc.subject.por.fl_str_mv su(1,1) algebra
SU(1,1) group
canonical transformations
coherent states
second quantization
pseudosphere
topic su(1,1) algebra
SU(1,1) group
canonical transformations
coherent states
second quantization
pseudosphere
description A basic introduction to the su(1,1) algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, we rather emphasize the existing connections between them. We discuss two parametrizations of the coherent states manifold SU(1,1)/U(1): as the Poincaré disk in the complex plane and as the pseudosphere (a sphere in a Minkowskian space), and show that it is a natural phase space for quantum systems with SU(1,1) symmetry.
publishDate 2004
dc.date.none.fl_str_mv 2004-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1806-11172004000400008
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Revista Brasileira de Ensino de Física v.26 n.4 2004
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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