Geometrisation of Fermions in Flat Spacetimes

Abstract

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.