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SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions
We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform [Formula: see text] mixing exterior-forms of all degrees and satisfying the chiral self-duality condition...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8945933/ https://www.ncbi.nlm.nih.gov/pubmed/35342281 http://dx.doi.org/10.1007/jhep04(2021)001 |
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author | Thierry-Mieg, Jean Jarvis, Peter |
author_facet | Thierry-Mieg, Jean Jarvis, Peter |
author_sort | Thierry-Mieg, Jean |
collection | PubMed |
description | We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform [Formula: see text] mixing exterior-forms of all degrees and satisfying the chiral self-duality condition [Formula: see text] , where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra. |
format | Online Article Text |
id | pubmed-8945933 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
record_format | MEDLINE/PubMed |
spelling | pubmed-89459332022-03-24 SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions Thierry-Mieg, Jean Jarvis, Peter J High Energy Phys Article We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform [Formula: see text] mixing exterior-forms of all degrees and satisfying the chiral self-duality condition [Formula: see text] , where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra. 2021-04 2021-04-01 /pmc/articles/PMC8945933/ /pubmed/35342281 http://dx.doi.org/10.1007/jhep04(2021)001 Text en https://creativecommons.org/publicdomain/zero/1.0/Open Access. As a work of the United States Government, this document is in the public domain within the United States. Additionally, the United States Government waives copyright and related rights in this work worldwide through the CC0 1.0 (https://creativecommons.org/publicdomain/zero/1.0/) Universal Public Domain Dedication. |
spellingShingle | Article Thierry-Mieg, Jean Jarvis, Peter SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
title | SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
title_full | SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
title_fullStr | SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
title_full_unstemmed | SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
title_short | SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
title_sort | su(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8945933/ https://www.ncbi.nlm.nih.gov/pubmed/35342281 http://dx.doi.org/10.1007/jhep04(2021)001 |
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