Dirac field in the eight-dimensional Kaluza-Klein theory

This paper considers the eight-dimensional Kaluza-Klein theory where the extra dimensions are a SU(2) x U(1) group manifold. A Dirac-field is coupled to the metric field. As a result we obtain that the four-dimensional theory is non-chiral and contains no-kind of Higgs mechanism to predict gauge bosons, quark and lepton masses and mixing angles, although it exhibit to possess all gauge bosons and fermionic isospin couplings for left-handed particles of a Weinberg-Salam theory in a curved space-time