Unified spin gauge theory of electroweak and gravitational interactions

Abstract

A spin gauge theory describing fundamental fermions and their electroweak and gravitational interactions is proposed. It is modelled on an eight-dimensional curved manifold M and uses its associated Clifford algebra. The elements of the algebra are represented by 16*16 matrices and the fermions are represented by sixteen-component column vectors. The frame field is introduced as a result of factorising the fermion mass term in the Lagrangian density and is included in an extended covariant derivative. The usual gauge theoretic technique of defining free bosonic Lagrangians from the fermion covariant derivative, when applied to the extended covariant derivative, gives the correct mass matrix for the photon, W and Z bosons, together with the Einstein-Hilbert gravitational Lagrangian density modified at short distances by a term quadratic in the curvature coefficients. Transformation of the Lagrangian by an inner automorphism of the Clifford algebra gives the correct mass and interaction terms for the up and down quarks.