Clifford Algebraic Unification of Conformal Gravity with an Extended Standard Model

Abstract:

A Clifford Cl(5 , C) unified gauge field theory formulation of conformal gravity and U(4) × U(4) × U(4) Yang–Mills in 4 D is elaborated further. It is shown how the Cl(5 , C) group has for physically relevant subgroup the one given by SU(2 , 2) × SU(4) C× SU(4) L× SU(4) R, and which is compatible with the Coleman–Mandula theorem (in the absence of a mass gap). The proposals presented here for a Clifford algebraic unification of conformal gravity with an extended standard model deal mainly with models of four generations of fermions. Mirror fermions can be incorporated as well. Whether these mirror fermions are dark matter candidates is an open question. There are also residual U(1) groups within this Clifford group unification scheme that should play an important role in cosmology in connection to dark matter particles coupled to gravity via a bimetric extension of general relativity. Other four generation scenarios based on Cl(6 , R) , Cl(8 , R) algebras, supersymmetric field theories and quaternions are discussed.

Año de publicación:

2017

Keywords:

• Grand unification
• Clifford algebras
• Yang–Mills
• Gravity

Fuente:

scopus