Exceptional quantum geometry and particle physics II

2018/08/24 by Michel Dubois-Violette, Ivan Todorov · 3 citations
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.QA #math.RA

paper · pdf · doi:10.1016/j.nuclphysb.2018.12.012

18 pages

arxiv created 2018/08/24 · arxiv updated 2018/12/26

Abstract

We continue the study undertaken in [13] of the relevance of the exceptional Jordan algebra J⁸₃ of hermitian 3× 3 octonionic matrices for the description of the internal space of the fundamental fermions of the Standard Model with 3 generations. By using the suggestion of [30] (properly justified here) that the Jordan algebra J⁸₂ of hermitian 2× 2 octonionic matrices is relevant for the description of the internal space of the fundamental fermions of one generation, we show that, based on the same principles and the same framework as in [13], there is a way to describe the internal space of the 3 generations which avoids the introduction of new fundamental fermions and where there is no problem with respect to the electroweak symmetry.

Cited by

• Higgs and Yukawa Structure in a Clifford Algebra Model with Three Generations and S₃ Family Symmetry
• Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry
• Octonions, complex structures and Standard Model fermions

Related

• Exceptional quantum algebra for the standard model of particle physics
• Exceptional quantum geometry and particle physics
• The Standard Model, The Exceptional Jordan Algebra, and Triality
• Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
• Octonions, exceptional Jordan algebra and the role of the group F₄ in particle physics