Exceptional quantum geometry and particle physics II

TL;DR

This paper explores the use of exceptional Jordan algebras to model the internal space of fundamental fermions in the Standard Model, extending previous work to three generations without introducing new particles.

Contribution

It proposes a framework using Jordan algebras to describe three fermion generations coherently within existing particle physics models.

Findings

Describes internal space of three generations without new fermions

Avoids electroweak symmetry issues in the model

Builds on previous algebraic approaches to particle physics

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.