Using the hydrodynamical formalism of quantum mechanics for a Schrodinger 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 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.

中文翻译：

---

波导论的几何解释和旋量场的表现

使用由 T. Takabayashi、JP Vigier 和追随者开发的涉及涡流的薛定谔旋转粒子的量子力学流体动力学形式，我们提出了波导理论的新几何解释。这种解释中的自旋波代表了一个客观真实的场，由波控制的物质粒子的演化是空间几何学的表现。我们假设这个场具有几何性质，基于这样的想法，即内在角动量，自旋，修改空间的几何形状，成为一个流形，表示为一个矢量丛，其基由平移坐标形成和时间，以及束的纤维，在每个点由四分体 $e^a_{\mu}$ 的场指定，由自旋波函数的双线性组合形成。结果表明，自旋矢量随着空间的测地线旋转而扭转，粒子根据几何化的引导方程运动。这个事实解释了自旋粒子的自作用。我们表明自旋矢量线的曲率和扭转由绝对平行几何的空间扭转决定。