The geometro-hydrodynamical representation of the torsion field

Abstract

We construct the geometro-hydrodynamical formalism for a spinning particle based on the six-dimensional manifold of autoparallelism geometry which is represented as a vector bundle with a base formed by the manifold of the translational coordinates and a fibre specified at each point by the field of an orthogonal coordinate frame underlying the classical spin. We show that the geometry of oriented points leads to the existence of torsion field with the source -the classical spin. We expand the geometro-hydrodynamical representation of Pauli field developed by Takabayasi and Vigier. We show that the external torsion field has a force effect on the velocity and spin fields via the spin-vorticity, which is characteristic of the space structure with the inhomogene triad field. The possible experimental effects of torsion field are discussed.

The Scattering of Dirac and Majorana Fermions in Spherically Symmetric Gravitational Field and Torsion Field

“…However the technique developed in this paper needs modification and extension to the cosmological torsion case. The geometrohydrodynamics approach may be employed to the prediction of neutrino propagation path in the FRW background with cosmic torsion distribution rather than the scattering of free neutrino by a localized torsion and curvature distribution [15,31,32].…”