Noncommutative quantum mechanics as a gauge theory

Detalhes bibliográficos
Autor(a) principal: Bemfica, Fábio Sperotto
Data de Publicação: 2009
Outros Autores: Girotti, Horacio Oscar
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/116134
Resumo: The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac’s method.
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spelling Bemfica, Fábio SperottoGirotti, Horacio Oscar2015-05-13T02:00:41Z20091550-7998http://hdl.handle.net/10183/116134000734112The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac’s method.application/pdfengPhysical review. D. Particles, fields, gravitation, and cosmology. College Park. Vol. 79, no. 12 (June 2009), 125024, 6 p.Mecânica quânticaEquação de DiracSistemas não comutativosTeoria de campos de calibresNoncommutative quantum mechanics as a gauge theoryEstrangeiroinfo: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:UFRGSORIGINAL000734112.pdf000734112.pdfTexto completo (inglês)application/pdf115351http://www.lume.ufrgs.br/bitstream/10183/116134/1/000734112.pdf3e245d715bcfb89a989c96de021fbf73MD51TEXT000734112.pdf.txt000734112.pdf.txtExtracted Texttext/plain32028http://www.lume.ufrgs.br/bitstream/10183/116134/2/000734112.pdf.txt8243527fcc721192799d7793bcdfd03dMD52THUMBNAIL000734112.pdf.jpg000734112.pdf.jpgGenerated Thumbnailimage/jpeg1905http://www.lume.ufrgs.br/bitstream/10183/116134/3/000734112.pdf.jpg554e3763320d5bc5763613fb9d8f0b16MD5310183/1161342023-08-02 03:34:11.408823oai:www.lume.ufrgs.br:10183/116134Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-08-02T06:34:11Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Noncommutative quantum mechanics as a gauge theory
title Noncommutative quantum mechanics as a gauge theory
spellingShingle Noncommutative quantum mechanics as a gauge theory
Bemfica, Fábio Sperotto
Mecânica quântica
Equação de Dirac
Sistemas não comutativos
Teoria de campos de calibres
title_short Noncommutative quantum mechanics as a gauge theory
title_full Noncommutative quantum mechanics as a gauge theory
title_fullStr Noncommutative quantum mechanics as a gauge theory
title_full_unstemmed Noncommutative quantum mechanics as a gauge theory
title_sort Noncommutative quantum mechanics as a gauge theory
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
Equação de Dirac
Sistemas não comutativos
Teoria de campos de calibres
topic Mecânica quântica
Equação de Dirac
Sistemas não comutativos
Teoria de campos de calibres
description The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac’s method.
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dc.relation.ispartof.pt_BR.fl_str_mv Physical review. D. Particles, fields, gravitation, and cosmology. College Park. Vol. 79, no. 12 (June 2009), 125024, 6 p.
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