New Path Equations in Absolute Parallelism Geometry

TL;DR

This paper generalizes the Bazanski approach to absolute parallelism geometry, deriving three path equations with torsion terms that suggest potential quantum features of paths in this geometry.

Contribution

It introduces a novel generalization of the Bazanski approach in absolute parallelism geometry, resulting in three new path equations with quantized torsion coefficients.

Findings

Derivation of three new path equations with torsion terms

Observation of stepwise changes in torsion coefficients

Speculation on quantum features of paths in absolute parallelism geometry

Abstract

The Bazanski approach, for deriving the geodesic equations in Riemannian geometry, is generalized in the absolute parallelism geometry. As a consequence of this generalization three path equations are obtained. A striking feature in the derived equations is the appearance of a torsion term with a numerical coefficients that jumps by a step of one half from equation to another. This is tempting to speculate that the paths in absolute parallelism geometry might admit a quantum feature.