Complex Boosts: A Hermitian Clifford Algebra Approach
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.8/3806 |
Resumo: | The aim of this paper is to study complex boosts in complex Minkowski space-time that preserves the Hermitian norm. Starting from the spin group Spin$^+(2n,2m,\bkR)$ in the real Minkowski space $\bkR^{2n,2m}$ we construct a Clifford realization of the pseudo-unitary group U$(n,m)$ using the space-time Witt basis in the framework of Hermitian Clifford algebra. Restricting to the case of one complex time direction we derive a general formula for a complex boost in an arbitrary complex direction and its $KAK-$decomposition, generalizing the well-known formula of a real boost in an arbitrary real direction. In the end we derive the complex Einstein velocity addition law for complex relativistic velocities, by the projective model of hyperbolic $n-$space. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Complex Boosts: A Hermitian Clifford Algebra ApproachPseudo-unitary groupComplex boostsHermitian Clifford algebraComplex Einstein velocity additionThe aim of this paper is to study complex boosts in complex Minkowski space-time that preserves the Hermitian norm. Starting from the spin group Spin$^+(2n,2m,\bkR)$ in the real Minkowski space $\bkR^{2n,2m}$ we construct a Clifford realization of the pseudo-unitary group U$(n,m)$ using the space-time Witt basis in the framework of Hermitian Clifford algebra. Restricting to the case of one complex time direction we derive a general formula for a complex boost in an arbitrary complex direction and its $KAK-$decomposition, generalizing the well-known formula of a real boost in an arbitrary real direction. In the end we derive the complex Einstein velocity addition law for complex relativistic velocities, by the projective model of hyperbolic $n-$space.Springer Nature [academic journals on nature.com]IC-OnlineFerreira, MiltonSommen, Franciscus2019-02-06T17:36:56Z2013-062013-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.8/3806engFerreira, M., and Sommen, F., Complex boosts: a Hermitian Clifford algebra approach, Adv. Appl. Clifford Algebras, 23(2), 2013, 339-3620188-70091661-490910.1007/s00006-012-0377-xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-17T15:47:58Zoai:iconline.ipleiria.pt:10400.8/3806Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:47:50.351437Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Complex Boosts: A Hermitian Clifford Algebra Approach |
title |
Complex Boosts: A Hermitian Clifford Algebra Approach |
spellingShingle |
Complex Boosts: A Hermitian Clifford Algebra Approach Ferreira, Milton Pseudo-unitary group Complex boosts Hermitian Clifford algebra Complex Einstein velocity addition |
title_short |
Complex Boosts: A Hermitian Clifford Algebra Approach |
title_full |
Complex Boosts: A Hermitian Clifford Algebra Approach |
title_fullStr |
Complex Boosts: A Hermitian Clifford Algebra Approach |
title_full_unstemmed |
Complex Boosts: A Hermitian Clifford Algebra Approach |
title_sort |
Complex Boosts: A Hermitian Clifford Algebra Approach |
author |
Ferreira, Milton |
author_facet |
Ferreira, Milton Sommen, Franciscus |
author_role |
author |
author2 |
Sommen, Franciscus |
author2_role |
author |
dc.contributor.none.fl_str_mv |
IC-Online |
dc.contributor.author.fl_str_mv |
Ferreira, Milton Sommen, Franciscus |
dc.subject.por.fl_str_mv |
Pseudo-unitary group Complex boosts Hermitian Clifford algebra Complex Einstein velocity addition |
topic |
Pseudo-unitary group Complex boosts Hermitian Clifford algebra Complex Einstein velocity addition |
description |
The aim of this paper is to study complex boosts in complex Minkowski space-time that preserves the Hermitian norm. Starting from the spin group Spin$^+(2n,2m,\bkR)$ in the real Minkowski space $\bkR^{2n,2m}$ we construct a Clifford realization of the pseudo-unitary group U$(n,m)$ using the space-time Witt basis in the framework of Hermitian Clifford algebra. Restricting to the case of one complex time direction we derive a general formula for a complex boost in an arbitrary complex direction and its $KAK-$decomposition, generalizing the well-known formula of a real boost in an arbitrary real direction. In the end we derive the complex Einstein velocity addition law for complex relativistic velocities, by the projective model of hyperbolic $n-$space. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-06 2013-06-01T00:00:00Z 2019-02-06T17:36:56Z |
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://hdl.handle.net/10400.8/3806 |
url |
http://hdl.handle.net/10400.8/3806 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ferreira, M., and Sommen, F., Complex boosts: a Hermitian Clifford algebra approach, Adv. Appl. Clifford Algebras, 23(2), 2013, 339-362 0188-7009 1661-4909 10.1007/s00006-012-0377-x |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer Nature [academic journals on nature.com] |
publisher.none.fl_str_mv |
Springer Nature [academic journals on nature.com] |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136972143329280 |