The Spinning Equations of Motion for Objects in AP-Geometry

TL;DR

This paper derives equations of spinning objects within Absolute Parallelism Geometry, offering a non-Riemannian framework that parallels the Papapetrou equations and explores spin tensor representation through geometric relations.

Contribution

It introduces a new set of spinning equations in AP-Geometry, extending the geometric description of spin beyond Riemannian frameworks.

Findings

Derived equations of spinning objects in AP-Geometry.

Established a geometric interpretation of the spin tensor.

Connected spin dynamics with path deviation in non-Riemannian geometry.

Abstract

Equations of spinning objects are obtained in Absolute Parallelism Geometry [AP], a special class of non-Riemannian geometry admitting an alternative non-vanishing curvature and torsion simultaneously. This new set of equations is the counterpart of the Papapetrou equations in the Riemannian geometry. Applying, the concept of geometerization of physics, it may give rise to describe the spin tensor as parameterized commutation relation between path and path deviation equations in both Riemannian and non-Riemannian geometries.