On the Kaluza-Klein geometrization of the Electro-Weak Model within a gauge theory of the 5-dimensional Lorentz group

Abstract

The geometrization of the Electro-Weak Model is achieved in a 5-dimensional Riemann-Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extra-coordinate and of a normalization factor. U(1) weak hyper-charge gauge fields are obtained from a Kaluza-Klein scheme, while the tetradic projections of the extra-dimensional contortion fields are interpreted as SU(2) weak isospin gauge fields. SU(2) generators are derived by the identification of the weak isospin current to the extra-dimensional current term in the Lagrangian density of the local Lorentz group. The geometrized U(1) and SU(2) groups will provide the proper transformation laws for bosonic and spinorial fields. Spin connections will be found to be purely Riemannian.