The Standard Model as an extension of the noncommutative algebra of forms

The Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra extension in the sense of Eilenberg. By doing so, they...

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Autores principales: Brouder, Christian, Bizi, Nadir, Besnard, Fabien
Lenguaje:eng
Publicado: 2015
Materias:
Particle Physics - Theory
Acceso en línea:http://cds.cern.ch/record/2009301
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author Brouder, Christian
Bizi, Nadir
Besnard, Fabien
author_facet Brouder, Christian
Bizi, Nadir
Besnard, Fabien
author_sort Brouder, Christian
collection CERN
description The Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra extension in the sense of Eilenberg. By doing so, they could deduce three axioms of the NCG Standard Model (i.e. order zero, order one and massless photon) from the single requirement that the extended algebra be associative. However, their approach was only applied to the finite part of the model because it fails for the full model. By taking into account the differential graded structure of the algebra of noncommutative differential forms, we obtain a formulation where the same three axioms are deduced from the associativity of the extended differential graded algebra, but which is now compatible with the full Standard Model.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2015
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spelling cern-20093012021-05-03T08:14:48Zhttp://cds.cern.ch/record/2009301engBrouder, ChristianBizi, NadirBesnard, FabienThe Standard Model as an extension of the noncommutative algebra of formsParticle Physics - TheoryThe Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra extension in the sense of Eilenberg. By doing so, they could deduce three axioms of the NCG Standard Model (i.e. order zero, order one and massless photon) from the single requirement that the extended algebra be associative. However, their approach was only applied to the finite part of the model because it fails for the full model. By taking into account the differential graded structure of the algebra of noncommutative differential forms, we obtain a formulation where the same three axioms are deduced from the associativity of the extended differential graded algebra, but which is now compatible with the full Standard Model.The Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra extension in the sense of Eilenberg. By doing so, they could deduce three axioms of the NCG Standard Model (i.e. order zero, order one and massless photon) from the single requirement that the extended algebra be associative. However, their approach was only applied to the finite algebra and fails the full model. By taking into account the differential graded structure of the algebra of noncommutative differential forms, we obtain a formulation where the same three axioms are deduced from the associativity of the extended differential graded algebra, but which is now also compatible with the full Standard Model. Finally, we present a Lorentzian version of the noncommutative geometry of the Standard Model and we show that the three axioms still hold if the four-dimensional manifold has a Lorentzian metric.arXiv:1504.03890oai:cds.cern.ch:20093012015-04-15
spellingShingle Particle Physics - Theory
Brouder, Christian
Bizi, Nadir
Besnard, Fabien
The Standard Model as an extension of the noncommutative algebra of forms
title The Standard Model as an extension of the noncommutative algebra of forms
title_full The Standard Model as an extension of the noncommutative algebra of forms
title_fullStr The Standard Model as an extension of the noncommutative algebra of forms
title_full_unstemmed The Standard Model as an extension of the noncommutative algebra of forms
title_short The Standard Model as an extension of the noncommutative algebra of forms
title_sort standard model as an extension of the noncommutative algebra of forms
topic Particle Physics - Theory
url http://cds.cern.ch/record/2009301
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AT brouderchristian standardmodelasanextensionofthenoncommutativealgebraofforms
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AT besnardfabien standardmodelasanextensionofthenoncommutativealgebraofforms

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