Spinor fields in general relativity

Abstract

A unitary field theory is developed with two fundamental field variables, a spinor and a bispinor-vector (set of Dirac matrices). The theory is required to be invariant under general co-ordinate transformations and similarity (spinor) transformations, and it is shown, under a minimum of restrictive hypotheses, that Einstein’s concept of teleparallelism is implied. Dirac’s equation is formulated in this unitary theory, and the electromagnetic field potentials are identified. An action density is proposed for the field which appears to exhibit gravitational and electromagnetic field properties consistent with experiment. There are indications that the charge of the elementary particles is quantized. Most of the paper is devoted to a specialization in which the ‘natural’ derivative of the Dirac matrices is made to vanish. The generalization of this theory is briefly considered at the end, and is found to introduce other fields, including a pseudo-scalar field which may account for nuclear forces.