Path Deviation Equations in AP-Geometry

TL;DR

This paper derives and analyzes deviation equations for paths in Absolute Parallelism geometry, comparing them to Riemannian geodesic deviation, with applications to quantum and gravitational phenomena.

Contribution

It introduces deviation equations in AP-geometry and compares them to Riemannian counterparts, expanding understanding of path behavior in alternative geometric frameworks.

Findings

Derived deviation equations in AP-geometry

Compared AP deviation equations with Riemannian geodesic deviation

Applied results to gravitational and quantum path phenomena

Abstract

Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret the discrepancy in the motion of thermal neutrons in the Earth's gravitational field (COW-experiment). The aim of the present work is to explore the properties of the deviation equations corresponding to these paths. In the present work the deviation equations are derived and compared to the geodesic deviation equation of the Riemannian geometry.