Geometrisation of Fermions in Semi-Riemannian Spacetimes

Abstract

An earlier scheme [arXiv:2404.03360], where torsion plays an essential part in a flat spacetime account of fermion spin, is extended to spacetimes with non-zero Riemann curvature. It is found that further essential features of the fermion, in particular its electromagnetic field, are determined by the curvature and torsion of spacetime. A natural model for the metric, singular along the spin axis of the particle, permits integration of a stress-energy tensor that fixes a realistic electron mass in terms of the Planck mass, despite the many orders of magnitude by which these values differ.