Geometrical interpretation of the wave-pilot theory and manifestation of the spinor fields

Mariya Iv Trukhanova, Gennady Shipov
2020 Progress of Theoretical and Experimental Physics  
Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle, developed by T. Takabayashi, J. P. Vigier and followers, that involves vortical flows, we propose the new geometrical interpretation of the wave-pilot theory. The spinor wave in this interpretation represents an objectively real field and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on
more » ... nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, that is represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of an tetrad $$e^a_{\mu}$$, forms from the bilinear combinations of spinor wave function. It was shown, that the spin vector rotates following the geodesic of the space with torsion and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.
doi:10.1093/ptep/ptaa106 fatcat:n7f6pyrisfd2xc26un5vhbk2be