Higgs field-fermion coupling in the tensor Dirac theory

In previous work, the Dirac and Einstein equations were unified in a tetrad formulation of a Kaluza-Klein model which gives precisely the usual Dirac-Einstein Lagrangian. In this model, the self-adjoint modes of the tetrad describe gravity, whereas the isometric modes of the tetrad together with a scalar field describe fermions. The tetrad Kaluza-Klein model is based on a constrained Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Psi is mapped to a set of SL(2, R) x U(1) gauge potentials A(alpha)(K) and a complex scalar field rho. In this paper we generalize the map Psi --> (A(alpha)(K), rho) to multiplets of n bispinor fields representing a fermion multiplet as in standard electroweak theory. We show that the Lagrangian for bispinor multiplets used in the Standard Model becomes a constrained Yang-Mills Lagrangian, for which the Higgs field determines a noninvariant gauge metric, thereby breaking the full gauge symmetry.