Exceptional quantum geometry and particle physics II

Michel Dubois-Violette; Ivan Todorov

doi:10.1016/j.nuclphysb.2018.12.012

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arXiv · 1808.08110

Exceptional quantum geometry and particle physics II

Michel Dubois-Violette·Ivan Todorov

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Abstract

We continue the study undertaken in [13] of the relevance of the exceptional Jordan algebra $J^8_3$ of hermitian $3\times 3$ 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 $J^8_2$ of hermitian $2\times 2$ 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.

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Michel Dubois-Violette, Ivan Todorov. 2018-08-24. Exceptional quantum geometry and particle physics II. https://doi.org/10.1016/j.nuclphysb.2018.12.012

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