On spinor connection in a riemannian space and the masses of elementary particles

Abstract

The transformation properties under time reversal of fundamental quaternion fields and the spin-affine connection in a Riemannian space are shown to lead to an eigenfunction equation whose eigenvalues can be identified with the masses of spinor particles. A one-to-one correspondence is established between the (co-ordinate-dependent) eigenvalues of this equation and a contraction of quaternion and spin-affine connection fields. The identification with theconstant mass of a spinor particle follows only after the coupled nonlinear spinor field equations uncouple, in the asymptotic limit in which the interactions between particles can be assumed to be vanishingly small. In this limit, a generally covariant form of the « free particle » Dirac equation emerges. A necessary part of the derivation is the demonstration of gauge invariance in the generally covariant spinor field equations.