The Riemann-Cartan space in the O-theory

TL;DR

This paper derives a nonrelativistic particle equation with spin in a nonassociative algebra framework, revealing the emergence of Riemann-Cartan space and torsion effects on gravitational attraction.

Contribution

It introduces a novel nonrelativistic spin particle model on a nonassociative algebra that naturally leads to Riemann-Cartan geometry with torsion.

Findings

Torsion interacts with particle spin in the model.

Torsion influences gravitational attraction strength.

Riemann-Cartan space arises from the algebraic framework.

Abstract

Nonrelativistic equation of particle with a spin for the Lagrangian on a nonassociative algebra is obtained. It is shown that in this model arises Riemann-Cartan space. In the case of central symmetry in addition to the pseudo-curvature appears torsion as pseudovector that interacts with the spin of the particle. An estimation of the influence of torsion on the strength of gravitational attraction in the central gravitational field is given.