Geometrization of the Electro-weak Model Bosonic Component

In this work, we develop a geometrical unification theory for gravity and the electro-weak model in a Kaluza-Klein approach; in particular, from the curvature dimensional reduction Einstein–Yang–Mills action is obtained. We consider two possible space-time manifolds: 1) V ⁴⊗ S ¹⊗ S ² where isospin doublets are identified with spinors; 2) V ⁴⊗ S ¹⊗ S ³ in which both quarks and leptons doublets can be recast into the same spinor, such that the equal number of quark generations and leptonic families is explained. Finally a self-interacting complex scalar field is introduced to reproduce the spontaneous symmetry breaking mechanism; in this respect, at the end, we get an Higgs fields whose two components have got opposite hypercharges.