Spin in a planar relativistic fermion problem
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.physleta.2021.127412 http://hdl.handle.net/11449/210326 |
Resumo: | In this work we seek to clarify the role of spin in a quantum relativistic two-dimensional world. To this end, we solve the Dirac equation for two-dimensional motion with circular symmetry using both 3+1 and 2+1 Dirac equations for a fermion interacting with a uniform magnetic field perpendicular to the plane of motion. We find that, as remarked already by other authors, the spin projection sin the direction of the magnetic field can be emulated in the 2+1 Hamiltonian as a parameter preserving the anti-commutation relations between the several terms in the Hamiltonian, although it is nota quantum number in the two-dimensional world. We also find that there is an equivalence between a pure vector potential and a pure tensor potential under circular symmetry, if the former is multiplied by s. This holds for any dependence on the polar coordinate rho. For the particular case of the uniform magnetic field, this means that this problem is equivalent to the two-dimensional Dirac oscillator. (C) 2021 Elsevier B.V. All rights reserved. |
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Repositório Institucional da UNESP |
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Spin in a planar relativistic fermion problem2+1 Dirac equationCircular symmetrySpinIn this work we seek to clarify the role of spin in a quantum relativistic two-dimensional world. To this end, we solve the Dirac equation for two-dimensional motion with circular symmetry using both 3+1 and 2+1 Dirac equations for a fermion interacting with a uniform magnetic field perpendicular to the plane of motion. We find that, as remarked already by other authors, the spin projection sin the direction of the magnetic field can be emulated in the 2+1 Hamiltonian as a parameter preserving the anti-commutation relations between the several terms in the Hamiltonian, although it is nota quantum number in the two-dimensional world. We also find that there is an equivalence between a pure vector potential and a pure tensor potential under circular symmetry, if the former is multiplied by s. This holds for any dependence on the polar coordinate rho. For the particular case of the uniform magnetic field, this means that this problem is equivalent to the two-dimensional Dirac oscillator. (C) 2021 Elsevier B.V. All rights reserved.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Estadual Paulista, Dept Fis, Campus Guaratingueta, BR-12516410 Guaratingueta, SP, BrazilUniv Coimbra, Phys Dept, CFisUC, P-3004516 Coimbra, PortugalUniv Estadual Paulista, Dept Fis, Campus Guaratingueta, BR-12516410 Guaratingueta, SP, BrazilCNPq: 09126/2019-3FAPESP: 2019/03626-4Elsevier B.V.Universidade Estadual Paulista (Unesp)Univ CoimbraCastro, A. S. de [UNESP]Alberto, P.2021-06-25T15:04:57Z2021-06-25T15:04:57Z2021-07-19info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article9http://dx.doi.org/10.1016/j.physleta.2021.127412Physics Letters A. Amsterdam: Elsevier, v. 404, 9 p., 2021.0375-9601http://hdl.handle.net/11449/21032610.1016/j.physleta.2021.127412WOS:000649677700001Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysics Letters Ainfo:eu-repo/semantics/openAccess2021-10-23T20:17:27Zoai:repositorio.unesp.br:11449/210326Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T20:17:27Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Spin in a planar relativistic fermion problem |
title |
Spin in a planar relativistic fermion problem |
spellingShingle |
Spin in a planar relativistic fermion problem Castro, A. S. de [UNESP] 2+1 Dirac equation Circular symmetry Spin |
title_short |
Spin in a planar relativistic fermion problem |
title_full |
Spin in a planar relativistic fermion problem |
title_fullStr |
Spin in a planar relativistic fermion problem |
title_full_unstemmed |
Spin in a planar relativistic fermion problem |
title_sort |
Spin in a planar relativistic fermion problem |
author |
Castro, A. S. de [UNESP] |
author_facet |
Castro, A. S. de [UNESP] Alberto, P. |
author_role |
author |
author2 |
Alberto, P. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Univ Coimbra |
dc.contributor.author.fl_str_mv |
Castro, A. S. de [UNESP] Alberto, P. |
dc.subject.por.fl_str_mv |
2+1 Dirac equation Circular symmetry Spin |
topic |
2+1 Dirac equation Circular symmetry Spin |
description |
In this work we seek to clarify the role of spin in a quantum relativistic two-dimensional world. To this end, we solve the Dirac equation for two-dimensional motion with circular symmetry using both 3+1 and 2+1 Dirac equations for a fermion interacting with a uniform magnetic field perpendicular to the plane of motion. We find that, as remarked already by other authors, the spin projection sin the direction of the magnetic field can be emulated in the 2+1 Hamiltonian as a parameter preserving the anti-commutation relations between the several terms in the Hamiltonian, although it is nota quantum number in the two-dimensional world. We also find that there is an equivalence between a pure vector potential and a pure tensor potential under circular symmetry, if the former is multiplied by s. This holds for any dependence on the polar coordinate rho. For the particular case of the uniform magnetic field, this means that this problem is equivalent to the two-dimensional Dirac oscillator. (C) 2021 Elsevier B.V. All rights reserved. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T15:04:57Z 2021-06-25T15:04:57Z 2021-07-19 |
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 |
http://dx.doi.org/10.1016/j.physleta.2021.127412 Physics Letters A. Amsterdam: Elsevier, v. 404, 9 p., 2021. 0375-9601 http://hdl.handle.net/11449/210326 10.1016/j.physleta.2021.127412 WOS:000649677700001 |
url |
http://dx.doi.org/10.1016/j.physleta.2021.127412 http://hdl.handle.net/11449/210326 |
identifier_str_mv |
Physics Letters A. Amsterdam: Elsevier, v. 404, 9 p., 2021. 0375-9601 10.1016/j.physleta.2021.127412 WOS:000649677700001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physics Letters A |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
9 |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science 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_ |
1797789404742287360 |