An AP-Structure with Finslerian Flavor: Path Equations

TL;DR

This paper derives new path equations within a Finslerian-inspired Absolute Parallelism geometry using the Bazanski approach, revealing potential quantum features and comparing with other geometric frameworks.

Contribution

It introduces a novel Finslerian flavor to Absolute Parallelism geometry and derives a unique set of path equations with a stepwise torsion coefficient.

Findings

Path equations exhibit torsion coefficient jumping by 0.5, suggesting quantum-like features.

Comparison with other geometries clarifies conditions for reducing to known path equations.

The approach generalizes Bazanski's method to new geometric contexts.

Abstract

The Bazanski approach for deriving paths is applied to Finsler geometry. The approach is generalized and applied to a new developed geometry called "Absolute parallelism with a Finslerian Flavor" (FAP). A sets of path equations is derived for the FAP. This is the horizontal (h) set. A striking feature appears in this set, that is: the coefficient of torsion term, in the set, jumps by a step of one-half from one equation to the other. This is tempting to believe that the h-set admits some quantum features. Comparisons with the corresponding sets in other geometries are given. Conditions to reduce the set of path equations obtained, to well known path equations in some geometries are summarized in a schematic diagram.