Daniel C. Galehouse
Department of Physics, University of Akron, Akron, OH 44230
Spinor coordinate space and Dirac theory
Coordinates from a real, conformally flat, eight-dimensional Riemannian
space are combined pairwise to give a four element complex valued vector that
transforms locally as a spinor. If the scalar curvature is set to zero, a
linear transformation to five dimensions, using anti-commuting matrices,
generates the Dirac equation. The single particle wave function is given by
the spinor gradient of the three-halves power of the conformal factor.
Gravitational and electromagnetic interactions are carried over from
five-dimensional theory. Additional physical effects are evident in the
geometry, and can be shown to involve the transmutation of an electron into a
neutrino by the weak interaction. Further developments may allow for the
description of more complicated phenomenology in particle physics.