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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2306.13098 |
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| _version_ | 1866914679447617536 |
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| author | Gresnigt, Niels G. Gourlay, Liam Varma, Abhinav |
| author_facet | Gresnigt, Niels G. Gourlay, Liam Varma, Abhinav |
| contents | An algebraic representation of three generations of fermions with $SU(3)_C$ color symmetry based on the Cayley-Dickson algebra of sedenions $\mathbb{S}$ is constructed. Recent constructions based on division algebras convincingly describe a single generation of leptons and quarks with Standard Model gauge symmetries. Nonetheless, an algebraic origin for the existence of exactly three generations has proven difficult to substantiate. We motivate $\mathbb{S}$ as a natural algebraic candidate to describe three generations with $SU(3)_C$ gauge symmetry. We initially represent one generation of leptons and quarks in terms of two minimal left ideals of $\mathbb{C}\ell(6)$, generated from a subset of all left actions of the complex sedenions on themselves. Subsequently we employ the finite group $S_3$, which are automorphisms of $\mathbb{S}$ but not of $\mathbb{O}$ to generate two additional generations. Given the relative obscurity of sedenions, efforts have been made to present the material in a self-contained manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13098 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions Gresnigt, Niels G. Gourlay, Liam Varma, Abhinav General Physics An algebraic representation of three generations of fermions with $SU(3)_C$ color symmetry based on the Cayley-Dickson algebra of sedenions $\mathbb{S}$ is constructed. Recent constructions based on division algebras convincingly describe a single generation of leptons and quarks with Standard Model gauge symmetries. Nonetheless, an algebraic origin for the existence of exactly three generations has proven difficult to substantiate. We motivate $\mathbb{S}$ as a natural algebraic candidate to describe three generations with $SU(3)_C$ gauge symmetry. We initially represent one generation of leptons and quarks in terms of two minimal left ideals of $\mathbb{C}\ell(6)$, generated from a subset of all left actions of the complex sedenions on themselves. Subsequently we employ the finite group $S_3$, which are automorphisms of $\mathbb{S}$ but not of $\mathbb{O}$ to generate two additional generations. Given the relative obscurity of sedenions, efforts have been made to present the material in a self-contained manner. |
| title | Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions |
| topic | General Physics |
| url | https://arxiv.org/abs/2306.13098 |