A New Class of Path Equations in AP-Geometry

TL;DR

This paper introduces a new class of path equations in AP-geometry derived via the Bazanski approach, revealing additional terms that relate to electromagnetic effects and potential quantum phenomena like the Aharanov-Bohm effect.

Contribution

It presents a novel class of path equations in AP-geometry with extra terms linked to electromagnetic potentials, expanding the understanding of particle motion in such geometries.

Findings

New path equations include four extra terms.

Extra terms relate to electromagnetic effects and quantum phenomena.

Vanishing of extra terms in torsion-less space-time.

Abstract

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the electromagnetic potential on the motion of the charged particle. This last term may give rise to an effect similar to the Aharanov-Bohm effect. It is to be considered that all extra terms will vanish if the space-time used is torsion-less.