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

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.

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Cited by in corpus (8)

• Conjugation Matters. Bioctonionic Veronese Vectors and Cayley-Rosenfeld Planes
• Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions
• Dixon-Rosenfeld Lines and the Standard Model
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• Listening to Celestial Algebras
• Physics with non-unital algebras? An invitation to the Okubo algebra
• Collineation groups of octonionic and split-octonionic planes
• The Resurgence of the G(2) Group for the Strong Sector and the Emergence of Dark Matter