Riemann-Cartan-Weyl geometries, quantum diffusions and the equivalence of the free maxwell and Dirac-Hestenes equations

We introduce the Riemann-Cartan-Weyl (RCW) space-time geometries of quantum mechanics with the most general trace-torsion non-exact Weyl 1-form, and characterize it in the Clifford bundle. Two electromagnetic potentials appear in the Weyl form, one having a zero field and the other one being the codifferential of a 2-form. We give the derivation of the non-linear equation for the wave function producing the exact Weyl one-form, which also defines the amplitude of a Dirac-Hestenes spinor operator field (DHSOF). We prove an equivalence between the free Maxwell equation for an extremal electromagnetic field and the Dirac-Hestenes equation for a DHSOF on a Riemann-Cartan-Weyl manifold, associating the electromagnetic potentials of the Weyl one-form with the internal electromagnetic potentials derived from the rotational dependance of a DHSOF. We show that this association produces a breaking of detailed balance in the spin plane. We discuss the relations with stochastic electrodynamics and the Navier-Stokes equation.