* Astronomy

Title: Intrinsic Dirac Behaviour of Scalar Curvature in a Complex Weyl-Cartan Geometry
Authors: J. E. Rankin

The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some sense, it appears to be possible to view the two component Dirac spinor as a single component, quaternionic, spacetime scalar. "Spin space" transformations become transformations of the internal quaternion basis. Essentially, quaternionic Dirac Theory projects into the complex plane neatly, where spin becomes related to the self-dual antisymmetric part of the metric. The correct Dirac eigenvalues and well-behaved eigenfunctions project intact into a pair of complex solutions for the scalar curvature in the earlier theory's Weyl-Cartan type geometry. Some estimates are made for predicted, interesting atomic and subatomic scale phenomena. A generalisation of the complex geometric structure to allow quaternionic gauges and curvatures is sketched in an appendix, and appears to be a fairly well defined possibility, but Dirac Theory seems to fit more naturally into the complex plane than into the full, generalized structure.

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