A Covariant Geometrical Representation of Quantum Interacting Electrons

Abstract

A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient. Anti-commuting matrices map the eight-dimensional waves into five dimensions. A projection into space time gives the known gravitational and electromagnetic forces. The electron transforms into a neutrino under hyper-rotations. First quantization is automatic. The theory is covariant and contains the known electron interactions.