Quantum Properties of a General Path Deviation Equation in the Pap-Geometry

TL;DR

This paper derives a quantum-influenced path deviation equation in PAP-geometry, incorporating curvature and torsion, which can describe deviations in particle trajectories and reduces to classical equations in Riemannian limits.

Contribution

It introduces a quantized path deviation equation in PAP-geometry that accounts for curvature and torsion effects, extending classical deviation equations.

Findings

Curvature and torsion terms are naturally quantized.

Increasing torsion decreases the effect of curvature on deviation.

Equation reduces to geodesic deviation in Riemannian geometry.

Abstract

A path deviation equation in the Parameterized Absolute Parallelism (PAP) geometry is derived. This equation includes curvature and torsion terms. These terms are found to be naturally quantized. The equation represents the deviation from a general path equation, in the PAP-geometry, derived by the author in a previous work. It is shown that, as the effect of the torsion, on the deviation, increases, the effect of the curvature decreases. It is also shown that the general path deviation equation can be reduced to the geodesic deviation equation if PAP-geometry becomes Riemannian. The equation can be used to study the deviation from the trajectories of spinning elementary particles.