Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry
Connes’ non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2015-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/2/023021 |
| _version_ | 1797751268557455360 |
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| author | Shane Farnsworth Latham Boyle |
| author_facet | Shane Farnsworth Latham Boyle |
| author_sort | Shane Farnsworth |
| collection | DOAJ |
| description | Connes’ non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U{{(1)}_{B-L}}$ gauge symmetry, and a single extra complex scalar field σ , which is a singlet under $SU{{(3)}_{C}}\times SU{{(2)}_{L}}\times U{{(1)}_{Y}}$ , but has $B-L=2$ . This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction. |
| first_indexed | 2024-03-12T16:45:00Z |
| format | Article |
| id | doaj.art-ea95d6099d3b484cbb85b5df8bf4917f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:45:00Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-ea95d6099d3b484cbb85b5df8bf4917f2023-08-08T14:17:58ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117202302110.1088/1367-2630/17/2/023021Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometryShane Farnsworth0Latham Boyle1Perimeter Institute for Theoretical Physics , Waterloo, Ontario N2L 2Y5, CanadaPerimeter Institute for Theoretical Physics , Waterloo, Ontario N2L 2Y5, CanadaConnes’ non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U{{(1)}_{B-L}}$ gauge symmetry, and a single extra complex scalar field σ , which is a singlet under $SU{{(3)}_{C}}\times SU{{(2)}_{L}}\times U{{(1)}_{Y}}$ , but has $B-L=2$ . This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.https://doi.org/10.1088/1367-2630/17/2/023021non-commutative geometrynon-associative geometrystandard model of particle physicsbeyond the standard model physicsB-L gauge symmetry |
| spellingShingle | Shane Farnsworth Latham Boyle Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry New Journal of Physics non-commutative geometry non-associative geometry standard model of particle physics beyond the standard model physics B-L gauge symmetry |
| title | Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry |
| title_full | Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry |
| title_fullStr | Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry |
| title_full_unstemmed | Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry |
| title_short | Rethinking Connes’ approach to the standard model of particle physics via non-commutative geometry |
| title_sort | rethinking connes approach to the standard model of particle physics via non commutative geometry |
| topic | non-commutative geometry non-associative geometry standard model of particle physics beyond the standard model physics B-L gauge symmetry |
| url | https://doi.org/10.1088/1367-2630/17/2/023021 |
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