# Path Equations In Absolute Parallelism Space

## TL;DR

This paper explores path equations in Absolute Parallelism space, demonstrating their derivation via a Bazanski-type Lagrangian, and discusses physical implications like spin-torsion interaction as an inherent property.

## Contribution

It provides a comprehensive treatment of path equations in AP-space using a novel Bazanski-type Lagrangian approach, linking geometric properties to physical interpretations.

## Key findings

- Path equations derived using Bazanski-type Lagrangian match conventional results.
- An expression conserved along curves in AP-space is identified.
- Spin-torsion interaction is shown to be an inherent property of AP-space.

## Abstract

Riemannian and Absolute Parallelism (AP) geometries are discussed. A lavish treatment of path equations in the AP-space using the Bazanski-type Lagrangian is presented; We write down an expression that is absolutely conserved along a curve in the AP-space and show that it gives the same path equations as obtained using the conventional Lagrangian formalism. We attribute physical interpretations to the resultant path equations and we show that the spin-torsion interaction is an inherent property of the AP-space.