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kodama

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- TL;DR Summary
- standard model octonions clifford alegbras

Quanta has this article,

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

John Baez has this

In this talk we review some lessons from grand unified theories and also from recent work using the

there are a lot of heavily cited research papers on using octonions and clifford alebgras to explain, among other things, that the 3 generations of fermions in the standard model is the result of octonions

and I would like to know where this line of research is and seems independent from string theory

Adam B. Gillard, Niels G. Gresnigt

N. Furey

[Submitted on 14 Feb 2017 (v1), last revised 8 May 2018 (this version, v3)]

Ovidiu Cristinel Stoica

### The Peculiar Math That Could Underlie the Laws of Nature

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

John Baez has this

### Can We Understand the Standard Model Using Octonions?

https://math.ucr.edu › home › baez › standard### Octonions and the Standard Model (Part 1) | The n-Category ...

https://golem.ph.utexas.edu › category › 2020/07 › oct...Jul 17, 2020 — I want to talk about some attempts to connect the*Standard Model*of particle physics to the*octonions*. I should start out by saying I don't .### Octonions and the Standard Model - Perimeter Events (Indico)

https://events.perimeterinstitute.ca › event › overviewFeb 8, 2021 — Over the years, various researchers have suggested connections between the*octonions*and the*standard model*of particle physics.In this talk we review some lessons from grand unified theories and also from recent work using the

*octonions*. The gauge group of the*Standard*...there are a lot of heavily cited research papers on using octonions and clifford alebgras to explain, among other things, that the 3 generations of fermions in the standard model is the result of octonions

and I would like to know where this line of research is and seems independent from string theory

### Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Adam B. Gillard, Niels G. Gresnigt

We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry SU(3)c×U(1)em can be described using the algebra of complexified sedenions C⊗S. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of C⊗S can be used to uniquely split the algebra into three complex octonion subalgebras C⊗O. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 C-dimensional C⊗O subalgebras on themselves generates three copies of the Clifford algebra Cℓ(6). It was previously shown that the minimal left ideals of Cℓ(6) describe a single generation of fermions with unbroken SU(3)c×U(1)em gauge symmetry. Extending this construction from C⊗O to C⊗S naturally leads to a description of exactly three generations.

Comments: | 22 pages, 2 figures |

Subjects: | High Energy Physics - Theory (hep-th) |

Cite as: | arXiv:1904.03186 [hep-th] |

### Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra

N. Furey

A considerable amount of the standard model's three-generation structure can be realized 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.

Finally, we close this discussion by outlining a proposal for how the standard model's full set of states might be identified within the left action maps of R⊗C⊗H⊗O (the Clifford algebra Cl(8)). Our aim is to include not only the standard model's three generations of quarks and leptons, but also its gauge bosons.

Comments: | 10 pages, 2 figures |

Subjects: | High Energy Physics - Theory (hep-th); High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph) |

Cite as: | arXiv:1910.08395 [hep-th] |

### High Energy Physics - Theory

[Submitted on 14 Feb 2017 (v1), last revised 8 May 2018 (this version, v3)]

### The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6

Ovidiu Cristinel Stoica

A simple geometric algebra is shown to contain automatically the leptons and quarks of a family of the Standard Model, and the electroweak and color gauge symmetries, without predicting extra particles and symmetries. The algebra is already naturally present in the Standard Model, in two instances of the Clifford algebra Cℓ6, one being algebraically generated by the Dirac algebra and the weak symmetry generators, and the other by a complex three-dimensional representation of the color symmetry, which generates a Witt decomposition which leads to the decomposition of the algebra into ideals representing leptons and quarks. The two instances being isomorphic, the minimal approach is to identify them, resulting in the model proposed here. The Dirac and Lorentz algebras appear naturally as subalgebras acting on the ideals representing leptons and quarks. The resulting representations on the ideals are invariant to the electromagnetic and color symmetries, which are generated by the bivectors of the algebra. The electroweak symmetry is also present, and it is already broken by the geometry of the algebra. The model predicts a bare Weinberg angle θW given by sin2θW=0.25. The model shares common ideas with previously known models, particularly with Chisholm and Farwell, 1996, Trayling and Baylis, 2004, and Furey, 2016.

Subjects: | High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Representation Theory (math.RT) |

Cite as: | arXiv:1702.04336 [hep-th] |