An Exceptional G(2) Extension of the Standard Model from the Correspondence with Cayley-Dickson Algebras Automorphism Groups

TL;DR

This paper proposes a novel algebraic approach linking Cayley-Dickson algebra automorphisms to particle physics symmetries, extending the Standard Model to include a G(2) gauge group and predicting new massive G(2)-gluons.

Contribution

It introduces a new criterion based on algebra automorphisms to extend the Standard Model, resulting in a G(2) gauge symmetry and associated particles.

Findings

Extension of the Standard Model gauge group to G(2)

Prediction of massive G(2)-gluons

Natural enlargement from SU(3) to G(2) symmetry

Abstract

In this article I propose a new criterion to extend the Standard Model of particle physics from a straightforward algebraic conjecture: the symmetries of physical microscopic forces originate from the automorphism groups of main Cayley-Dickson algebras, from complex numbers to octonions and sedenions. This correspondence leads to a natural enlargement of the Standard Model color sector, from a SU(3) gauge group to an exceptional Higgs-broken G(2) group, following the octonionic automorphism relation guideline. In this picture, an additional ensemble of massive G(2)-gluons emerges, which is separated from the particle dynamics of the Standard Model.