Noncommutative quantum mechanics : uniqueness of the functional description

Detalhes bibliográficos
Autor(a) principal: Bemfica, Fábio Sperotto
Data de Publicação: 2008
Outros Autores: Girotti, Horacio Oscar
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/116133
Resumo: The generalized Weyl transform of index is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter . We succeed in proving that the -dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the α-dependent terms.
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spelling Bemfica, Fábio SperottoGirotti, Horacio Oscar2015-05-13T02:00:41Z20081550-7998http://hdl.handle.net/10183/116133000734098The generalized Weyl transform of index is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter . We succeed in proving that the -dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the α-dependent terms.application/pdfengPhysical review. D. Particles, fields, gravitation, and cosmology. College Park. Vol. 78, no. 12 (Dec. 2008), 125009, 6 p.Mecânica quânticaTeoria quânticaSistemas não comutativosNoncommutative quantum mechanics : uniqueness of the functional descriptionEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000734098.pdf000734098.pdfTexto completo (inglês)application/pdf95810http://www.lume.ufrgs.br/bitstream/10183/116133/1/000734098.pdff6c92b6b813e7cd27ad3b68ac4f69555MD51TEXT000734098.pdf.txt000734098.pdf.txtExtracted Texttext/plain20157http://www.lume.ufrgs.br/bitstream/10183/116133/2/000734098.pdf.txtecf480a1fc0a25b6a61484a7552b0046MD52THUMBNAIL000734098.pdf.jpg000734098.pdf.jpgGenerated Thumbnailimage/jpeg1924http://www.lume.ufrgs.br/bitstream/10183/116133/3/000734098.pdf.jpg0bd6a13ee8a775c3030c94b48e37fa4eMD5310183/1161332023-08-02 03:33:00.291955oai:www.lume.ufrgs.br:10183/116133Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-08-02T06:33Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Noncommutative quantum mechanics : uniqueness of the functional description
title Noncommutative quantum mechanics : uniqueness of the functional description
spellingShingle Noncommutative quantum mechanics : uniqueness of the functional description
Bemfica, Fábio Sperotto
Mecânica quântica
Teoria quântica
Sistemas não comutativos
title_short Noncommutative quantum mechanics : uniqueness of the functional description
title_full Noncommutative quantum mechanics : uniqueness of the functional description
title_fullStr Noncommutative quantum mechanics : uniqueness of the functional description
title_full_unstemmed Noncommutative quantum mechanics : uniqueness of the functional description
title_sort Noncommutative quantum mechanics : uniqueness of the functional description
author Bemfica, Fábio Sperotto
author_facet Bemfica, Fábio Sperotto
Girotti, Horacio Oscar
author_role author
author2 Girotti, Horacio Oscar
author2_role author
dc.contributor.author.fl_str_mv Bemfica, Fábio Sperotto
Girotti, Horacio Oscar
dc.subject.por.fl_str_mv Mecânica quântica
Teoria quântica
Sistemas não comutativos
topic Mecânica quântica
Teoria quântica
Sistemas não comutativos
description The generalized Weyl transform of index is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter . We succeed in proving that the -dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the α-dependent terms.
publishDate 2008
dc.date.issued.fl_str_mv 2008
dc.date.accessioned.fl_str_mv 2015-05-13T02:00:41Z
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dc.relation.ispartof.pt_BR.fl_str_mv Physical review. D. Particles, fields, gravitation, and cosmology. College Park. Vol. 78, no. 12 (Dec. 2008), 125009, 6 p.
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