Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra
A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3)⊕u(1)...
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Elsevier
2018-10-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269318306452 |
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doaj-791e5cfddcb74132a0fd3ce8482546722020-11-25T00:35:18ZengElsevierPhysics Letters B0370-26932018-10-017858489Three generations, two unbroken gauge symmetries, and one eight-dimensional algebraC. Furey0Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK; Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK; Correspondence to: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK.A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3)⊕u(1) action which splits this 64C-dimensional space into complexified generators of SU(3), together with 48 states. These 48 states exhibit the behaviour of exactly three generations of quarks and leptons under the standard model's two unbroken gauge symmetries. This article builds on a previous one, [1], by incorporating electric charge.http://www.sciencedirect.com/science/article/pii/S0370269318306452 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
C. Furey |
| spellingShingle |
C. Furey Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra Physics Letters B |
| author_facet |
C. Furey |
| author_sort |
C. Furey |
| title |
Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra |
| title_short |
Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra |
| title_full |
Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra |
| title_fullStr |
Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra |
| title_full_unstemmed |
Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra |
| title_sort |
three generations, two unbroken gauge symmetries, and one eight-dimensional algebra |
| publisher |
Elsevier |
| series |
Physics Letters B |
| issn |
0370-2693 |
| publishDate |
2018-10-01 |
| description |
A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3)⊕u(1) action which splits this 64C-dimensional space into complexified generators of SU(3), together with 48 states. These 48 states exhibit the behaviour of exactly three generations of quarks and leptons under the standard model's two unbroken gauge symmetries. This article builds on a previous one, [1], by incorporating electric charge. |
| url |
http://www.sciencedirect.com/science/article/pii/S0370269318306452 |
| work_keys_str_mv |
AT cfurey threegenerationstwounbrokengaugesymmetriesandoneeightdimensionalalgebra |
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1725309147157626880 |