The Dirac equation in a non-Riemannian manifold III: An analysis using the algebra of quaternions and octonions

Abstract

The geometrical properties of a flat tangent space-time local to the manifold of the Einstein–Schrödinger nonsymmetric theory to which an internal octonionic space is attached, is developed here. As an application of the theory, an octonionic Dirac equation for a spin-1/2 particle is also obtained, where is now used an octonionic-like gauge field. It is shown that the (quaternionic) nonsymmetric Yang–Mills theory can be easily recovered and from there, the usual gauge theory on a curved space.