The Standard Model, The Exceptional Jordan Algebra, and Triality

• URL: http://arxiv.org/abs/2006.16265v1
• Date: Mon, 29 Jun 2020 18:00:06 GMT
• Title: The Standard Model, The Exceptional Jordan Algebra, and Triality
• Authors: Latham Boyle
• Abstract summary: We point out an intriguing relationship between the complexification of this algebra and the standard model of particle physics. This suggests a geometric interpretation, where a single generation of standard model fermions is described by the tangent space $(mathbbCotimesmathbbO)2$ of the complex octonionic projective plane.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing relationship between the complexification of this algebra and the standard model of particle physics, its minimal left-right-symmetric $SU(3)\times SU(2)_{L}\times SU(2)_{R}\times U(1)$ extension, and $Spin(10)$ unification. This suggests a geometric interpretation, where a single generation of standard model fermions is described by the tangent space $(\mathbb{C}\otimes\mathbb{O})^{2}$ of the complex octonionic projective plane, and the existence of three generations is related to $SO(8)$ triality.

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