Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework

Autores
Cirilo, Diego Julio
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in this UFT general context that the underlying basis of the single geometrical structure P (G, M) (the principal fiber bundle over the real spacetime manifold M with structural group G) reflecting the symmetries of the different fields carry naturally a biquaternionic structure instead of a complex one. This fact allows us to analyze algebraically and to interpret physically in a straighforward way the Majorana and Dirac representations and the relation of such structures with the spacetime signature and non-hermitian (CP) dynamic operators. Also, from the underlying structure of the tangent space, the existence of hidden (super) symmetries and the possibility of supersymmetric extensions of these UFT models are given showing that Rothstein’s theorem is incomplete for that description. The importance of the Clifford algebras in the description of all symmetries, mainly the interaction of gravity with the other fields, is briefly discussed.
Fil: Cirilo, Diego Julio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física del Plasma. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física del Plasma; Argentina. Joint Institute for Nuclear Research; Rusia
Materia
Unified Field Theories
Affine Geometries
Dirac-Majorana
Poisson Manifolds
Supermanifolds
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19289

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spelling Algebraic Structures, Physics and Geometry from a Unified Field Theoretical FrameworkCirilo, Diego JulioUnified Field TheoriesAffine GeometriesDirac-MajoranaPoisson ManifoldsSupermanifoldshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in this UFT general context that the underlying basis of the single geometrical structure P (G, M) (the principal fiber bundle over the real spacetime manifold M with structural group G) reflecting the symmetries of the different fields carry naturally a biquaternionic structure instead of a complex one. This fact allows us to analyze algebraically and to interpret physically in a straighforward way the Majorana and Dirac representations and the relation of such structures with the spacetime signature and non-hermitian (CP) dynamic operators. Also, from the underlying structure of the tangent space, the existence of hidden (super) symmetries and the possibility of supersymmetric extensions of these UFT models are given showing that Rothstein’s theorem is incomplete for that description. The importance of the Clifford algebras in the description of all symmetries, mainly the interaction of gravity with the other fields, is briefly discussed.Fil: Cirilo, Diego Julio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física del Plasma. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física del Plasma; Argentina. Joint Institute for Nuclear Research; RusiaSpringer2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19289Cirilo, Diego Julio; Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework; Springer; International Journal of Theoretical Physics; 54; 10; 10-2015; 3713-37270020-77481572-9575CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10773-015-2609-zinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10773-015-2609-zinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1411.5493info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:40Zoai:ri.conicet.gov.ar:11336/19289instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:18:41.125CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
title Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
spellingShingle Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
Cirilo, Diego Julio
Unified Field Theories
Affine Geometries
Dirac-Majorana
Poisson Manifolds
Supermanifolds
title_short Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
title_full Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
title_fullStr Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
title_full_unstemmed Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
title_sort Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework
dc.creator.none.fl_str_mv Cirilo, Diego Julio
author Cirilo, Diego Julio
author_facet Cirilo, Diego Julio
author_role author
dc.subject.none.fl_str_mv Unified Field Theories
Affine Geometries
Dirac-Majorana
Poisson Manifolds
Supermanifolds
topic Unified Field Theories
Affine Geometries
Dirac-Majorana
Poisson Manifolds
Supermanifolds
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in this UFT general context that the underlying basis of the single geometrical structure P (G, M) (the principal fiber bundle over the real spacetime manifold M with structural group G) reflecting the symmetries of the different fields carry naturally a biquaternionic structure instead of a complex one. This fact allows us to analyze algebraically and to interpret physically in a straighforward way the Majorana and Dirac representations and the relation of such structures with the spacetime signature and non-hermitian (CP) dynamic operators. Also, from the underlying structure of the tangent space, the existence of hidden (super) symmetries and the possibility of supersymmetric extensions of these UFT models are given showing that Rothstein’s theorem is incomplete for that description. The importance of the Clifford algebras in the description of all symmetries, mainly the interaction of gravity with the other fields, is briefly discussed.
Fil: Cirilo, Diego Julio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física del Plasma. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física del Plasma; Argentina. Joint Institute for Nuclear Research; Rusia
description Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in this UFT general context that the underlying basis of the single geometrical structure P (G, M) (the principal fiber bundle over the real spacetime manifold M with structural group G) reflecting the symmetries of the different fields carry naturally a biquaternionic structure instead of a complex one. This fact allows us to analyze algebraically and to interpret physically in a straighforward way the Majorana and Dirac representations and the relation of such structures with the spacetime signature and non-hermitian (CP) dynamic operators. Also, from the underlying structure of the tangent space, the existence of hidden (super) symmetries and the possibility of supersymmetric extensions of these UFT models are given showing that Rothstein’s theorem is incomplete for that description. The importance of the Clifford algebras in the description of all symmetries, mainly the interaction of gravity with the other fields, is briefly discussed.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/19289
Cirilo, Diego Julio; Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework; Springer; International Journal of Theoretical Physics; 54; 10; 10-2015; 3713-3727
0020-7748
1572-9575
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19289
identifier_str_mv Cirilo, Diego Julio; Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework; Springer; International Journal of Theoretical Physics; 54; 10; 10-2015; 3713-3727
0020-7748
1572-9575
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10773-015-2609-z
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10773-015-2609-z
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1411.5493
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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