On Jordan–Clifford Algebras, Three Fermion Generations with Higgs Fields and a SU (3) × SU (2) <inf>L</inf>× SU (2) <inf>R</inf>× U (1) Model

Abstract:

Previously we have shown that the algebra J3[C⊗O]⊗Cℓ(4,C),given by the tensor product of the complex exceptional Jordan J3[C⊗ O] and the complex Clifford algebra Cℓ(4 , C) , can describe all of the spinorial degrees of freedom of three generations of fermions in four-space-time dimensions. We extend our construction to show that it also includes the degrees of freedom of three sets of pairs of complex scalar Higgs-doublets {HL(m),HR(m)};m=1,2,3, and their CPT conjugates. Furthermore, a close inspection of the fermion structure of each generation reveals that it fits naturally with the sixteen complex-dimensional representation of the internal left/right symmetric gauge group GLR= SU (3) C× SU (2) L× SU (2) R× U (1). It is reviewed how the latter group emerges from the intersection of SO (10) and SU (3) × SU (3) × SU (3) in E6. In the concluding remarks we briefly discuss the role that the extra Higgs fields may have as dark matter candidates; the construction of Chern–Simons-like matrix cubic actions; hexaquarks; supersymmetry and Clifford bundles over the complex-octonionic projective plane (C⊗ O) P2 whose isometry group is E6.

Año de publicación:

2021

Keywords:

• Division Algebra
• dark matter
• Jordan algebras
• Clifford algebra
• Higgs field
• Extension of the Standard Model

Fuente:

scopus