Elko spinor fields: Lagrangians for gravity derived from supergravity

Detalhes bibliográficos
Autor(a) principal: Da Rocha, Roldão
Data de Publicação: 2009
Outros Autores: Hoff Da Silva, J. M. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1142/S0219887809003618
http://hdl.handle.net/11449/225493
Resumo: Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong - together with Majorana spinor fields - to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that - in particular - the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator - leading ELKO Lagrangian into the Dirac Lagrangian - is also pointed out, together with its relationship to the instanton Hopf fibration. © 2009 World Scientific Publishing Company.
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spelling Elko spinor fields: Lagrangians for gravity derived from supergravityEinstein-Hilbert actionELKO spinor fieldsQuadratic Spinor LagrangianSpin-Clifford bundlesSupergravityDual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong - together with Majorana spinor fields - to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that - in particular - the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator - leading ELKO Lagrangian into the Dirac Lagrangian - is also pointed out, together with its relationship to the instanton Hopf fibration. © 2009 World Scientific Publishing Company.Centro de Matemática, Computação e Cognição Universidade Federal do ABC, 09210-170 Santo André, SPInstituto de Física Teórica Universidade Estadual Paulista, Rua Pamplona 145 01405-900, São Paulo, SPInstituto de Física Teórica Universidade Estadual Paulista, Rua Pamplona 145 01405-900, São Paulo, SPUniversidade Federal do ABC (UFABC)Universidade Estadual Paulista (UNESP)Da Rocha, RoldãoHoff Da Silva, J. M. [UNESP]2022-04-28T20:52:17Z2022-04-28T20:52:17Z2009-06-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article461-477http://dx.doi.org/10.1142/S0219887809003618International Journal of Geometric Methods in Modern Physics, v. 6, n. 3, p. 461-477, 2009.0219-8878http://hdl.handle.net/11449/22549310.1142/S02198878090036182-s2.0-66949125044Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Geometric Methods in Modern Physicsinfo:eu-repo/semantics/openAccess2022-04-28T20:52:17Zoai:repositorio.unesp.br:11449/225493Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:53:25.700008Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Elko spinor fields: Lagrangians for gravity derived from supergravity
title Elko spinor fields: Lagrangians for gravity derived from supergravity
spellingShingle Elko spinor fields: Lagrangians for gravity derived from supergravity
Da Rocha, Roldão
Einstein-Hilbert action
ELKO spinor fields
Quadratic Spinor Lagrangian
Spin-Clifford bundles
Supergravity
title_short Elko spinor fields: Lagrangians for gravity derived from supergravity
title_full Elko spinor fields: Lagrangians for gravity derived from supergravity
title_fullStr Elko spinor fields: Lagrangians for gravity derived from supergravity
title_full_unstemmed Elko spinor fields: Lagrangians for gravity derived from supergravity
title_sort Elko spinor fields: Lagrangians for gravity derived from supergravity
author Da Rocha, Roldão
author_facet Da Rocha, Roldão
Hoff Da Silva, J. M. [UNESP]
author_role author
author2 Hoff Da Silva, J. M. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Federal do ABC (UFABC)
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Da Rocha, Roldão
Hoff Da Silva, J. M. [UNESP]
dc.subject.por.fl_str_mv Einstein-Hilbert action
ELKO spinor fields
Quadratic Spinor Lagrangian
Spin-Clifford bundles
Supergravity
topic Einstein-Hilbert action
ELKO spinor fields
Quadratic Spinor Lagrangian
Spin-Clifford bundles
Supergravity
description Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong - together with Majorana spinor fields - to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that - in particular - the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator - leading ELKO Lagrangian into the Dirac Lagrangian - is also pointed out, together with its relationship to the instanton Hopf fibration. © 2009 World Scientific Publishing Company.
publishDate 2009
dc.date.none.fl_str_mv 2009-06-17
2022-04-28T20:52:17Z
2022-04-28T20:52:17Z
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/10.1142/S0219887809003618
International Journal of Geometric Methods in Modern Physics, v. 6, n. 3, p. 461-477, 2009.
0219-8878
http://hdl.handle.net/11449/225493
10.1142/S0219887809003618
2-s2.0-66949125044
url http://dx.doi.org/10.1142/S0219887809003618
http://hdl.handle.net/11449/225493
identifier_str_mv International Journal of Geometric Methods in Modern Physics, v. 6, n. 3, p. 461-477, 2009.
0219-8878
10.1142/S0219887809003618
2-s2.0-66949125044
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal of Geometric Methods in Modern Physics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 461-477
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
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