Noncommutative quantum mechanics as a gauge theory
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
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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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. |
publishDate |
2009 |
dc.date.issued.fl_str_mv |
2009 |
dc.date.accessioned.fl_str_mv |
2015-05-13T02:00:41Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
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article |
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publishedVersion |
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http://hdl.handle.net/10183/116134 |
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1550-7998 |
dc.identifier.nrb.pt_BR.fl_str_mv |
000734112 |
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http://hdl.handle.net/10183/116134 |
dc.language.iso.fl_str_mv |
eng |
language |
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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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openAccess |
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