Discretizing the deformation parameter in the suq(2) quantum algebra
Autor(a) principal: | |
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Data de Publicação: | 1998 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://hdl.handle.net/11449/223875 |
Resumo: | Inspired in recent works of Biedenharn [1, 2] on the realization of the q-algebra suq (2), we show in this note that the condition [2j + 1]q = Nq(j) = integer, implies the discretization of the deformation parameter α, where q = eα. This discretization replaces the continuum associated to α by an infinite sequence α1, α2, α3, ..., obtained for the values of j, which label the irreps of suq(2). The algebraic properties of Nq(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of α. |
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Repositório Institucional da UNESP |
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Discretizing the deformation parameter in the suq(2) quantum algebraParameter discretizationQuantum algebrassuq(2)Inspired in recent works of Biedenharn [1, 2] on the realization of the q-algebra suq (2), we show in this note that the condition [2j + 1]q = Nq(j) = integer, implies the discretization of the deformation parameter α, where q = eα. This discretization replaces the continuum associated to α by an infinite sequence α1, α2, α3, ..., obtained for the values of j, which label the irreps of suq(2). The algebraic properties of Nq(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of α.Inst. de Fisica Teorica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, São Paulo, S.P.Inst. de Fisica Teorica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, São Paulo, S.P.Universidade Estadual Paulista (UNESP)Palladino, B. E. [UNESP]Ferreira, P. Leal [UNESP]2022-04-28T19:53:29Z2022-04-28T19:53:29Z1998-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article73-77Revista Mexicana de Fisica, v. 44, n. 1, p. 73-77, 1998.0035-001Xhttp://hdl.handle.net/11449/2238752-s2.0-0008090357Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengRevista Mexicana de Fisicainfo:eu-repo/semantics/openAccess2022-04-28T19:53:29Zoai:repositorio.unesp.br:11449/223875Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:47:24.395082Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Discretizing the deformation parameter in the suq(2) quantum algebra |
title |
Discretizing the deformation parameter in the suq(2) quantum algebra |
spellingShingle |
Discretizing the deformation parameter in the suq(2) quantum algebra Palladino, B. E. [UNESP] Parameter discretization Quantum algebras suq(2) |
title_short |
Discretizing the deformation parameter in the suq(2) quantum algebra |
title_full |
Discretizing the deformation parameter in the suq(2) quantum algebra |
title_fullStr |
Discretizing the deformation parameter in the suq(2) quantum algebra |
title_full_unstemmed |
Discretizing the deformation parameter in the suq(2) quantum algebra |
title_sort |
Discretizing the deformation parameter in the suq(2) quantum algebra |
author |
Palladino, B. E. [UNESP] |
author_facet |
Palladino, B. E. [UNESP] Ferreira, P. Leal [UNESP] |
author_role |
author |
author2 |
Ferreira, P. Leal [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Palladino, B. E. [UNESP] Ferreira, P. Leal [UNESP] |
dc.subject.por.fl_str_mv |
Parameter discretization Quantum algebras suq(2) |
topic |
Parameter discretization Quantum algebras suq(2) |
description |
Inspired in recent works of Biedenharn [1, 2] on the realization of the q-algebra suq (2), we show in this note that the condition [2j + 1]q = Nq(j) = integer, implies the discretization of the deformation parameter α, where q = eα. This discretization replaces the continuum associated to α by an infinite sequence α1, α2, α3, ..., obtained for the values of j, which label the irreps of suq(2). The algebraic properties of Nq(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of α. |
publishDate |
1998 |
dc.date.none.fl_str_mv |
1998-01-01 2022-04-28T19:53:29Z 2022-04-28T19:53:29Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
Revista Mexicana de Fisica, v. 44, n. 1, p. 73-77, 1998. 0035-001X http://hdl.handle.net/11449/223875 2-s2.0-0008090357 |
identifier_str_mv |
Revista Mexicana de Fisica, v. 44, n. 1, p. 73-77, 1998. 0035-001X 2-s2.0-0008090357 |
url |
http://hdl.handle.net/11449/223875 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Revista Mexicana de Fisica |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
73-77 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128979604865024 |