Structure and Solutions of a Unified Theory of Gravitation and Symmetry Violation

Abstract

The structure of a unified theory of gravitation and symmetry violation of $U(3)$ [or $U(3)\ensuremath{\bigotimes}U(3)$] is studied, and exact solutions for the symmetry-breaking fields are obtained. These solutions are then investigated in the absence of gravitational fields by expanding the nonlinear symmetry-breaking equations in powers of a small parameter $\ensuremath{\lambda}$. It is shown that the resulting nonlinear equations can be solved, in association with the divergence equations for weak vector (or axial-vector) current densities, to determine by iteration the breaking to any order. It is found that the breaking to first order, determined by linear equations, is caused by zero-mass particles. In the case of $\mathrm{SU}(2)$, in the linear approximation, equations consistent with Maxwell's electrodynamics and the correct form of the divergence equation for the isotopic-spin current are obtained.