William J. Leigh | Searcharxiv

arXiv2024

Geometrisation of Fermions in Semi-Riemannian Spacetimes

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.

gr-qc↗

arXiv2024

Geometrisation of Fermions in Flat Spacetimes

Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a spinor identity that closely resembles the Dirac equation of quantum electrodynamics. All relevant integrals involving solutions of the spinor identity converge and require that the spin, which is no longer intrinsic but arises from circulating currents, be 1/2 whilst the magnetic moment takes the quantum value of 1 magneton, characteristic of an isolated Dirac particle. The underlying torsion associates the otherwise strictly localised particle with an extended spacetime structure that may be relevant to wider quantum phenomena.

hep-th↗