The Dirac equation in a non-Riemannian manifold: II. An analysis using an internal local n-dimensional space of the Yang–Mills type

Abstract

The geometrical properties of a flat tangent space-time local to the generalized manifold of the Einstein–Schrödinger nonsymmetric theory, with an internal n-dimensional space with the SU(n) symmetry group, is developed here. As an application of the theory, a generalized Dirac equation, where the electromagnetic and the Yang–Mills fields are included in a more complex field equation, is then obtained. When the two-dimensional case is considered, the theory can be immediately interpreted through the algebra of quaternions, which, through the Hurwitz theorem, presupposes a generalization of the theory using the algebra of octonions.