# The Geometro-Hydrodynamical Representation of the Torsion Field

## TL;DR

This paper develops a geometric formalism for spinning particles that incorporates torsion fields sourced by classical spin, revealing how torsion influences particle velocity and spin dynamics, with potential experimental implications.

## Contribution

It introduces a geometro-hydrodynamical formalism based on autoparallelism geometry to describe torsion fields generated by classical spin, extending previous models.

## Key findings

- Torsion field affects velocity and spin via spin-vorticity.
- The formalism links geometry with classical spin and torsion.
- Potential experimental effects of torsion are discussed.

## 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.