Higgs Field—Fermion Coupling in the Tensor Dirac Theory

Abstract

In previous work, the Dirac and Einstein equations were unified in a tetradformulation of a Kaluza—Klein model which gives precisely the usualDirac—Einstein Lagrangian. In this model, the self-adjoint modes of the tetraddescribe gravity, whereas the isometric modes of the tetrad together with a scalarfield describe fermions. The tetrad Kaluza—Klein model is based on a constrainedYang—Mills formulation of the Dirac Lagrangian in which the bispinor field Ψis mapped to a set of SL(2, R) × U(1) gauge potentialsAKa and a complex scalarfield ρ. In this paper we generalize the map Ψ →(AKa, ρ) to multiplets of nbispinor fields representing a fermion multiplet as in standard electroweak theory.We show that the Lagrangian for bispinor multiplets used in the Standard Modelbecomes a constrained Yang—Mills Lagrangian, for which the Higgs fielddetermines a noninvariant gauge metric, thereby breaking the full gauge symmetry.