Motion of Charged Spinning Particles in a Unified Field

TL;DR

This paper introduces a new geometric curve in PAP-geometry that models the trajectories of charged and spinning particles in unified fields, incorporating electromagnetic effects directly into the motion equations.

Contribution

It develops a novel curve in PAP-geometry that generalizes particle trajectories, including electromagnetic interactions, within a unified field theoretical framework.

Findings

The new curve reduces to geodesics for scalar particles.

The curve incorporates electromagnetic potential and Lorentz terms.

Physical implications of the electromagnetic term are discussed.

Abstract

Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP-) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a trajectory of charged spinning test particle in any unified field theory constructed in the PAP-space. We show that imposing certain conditions on the two parameters, the new curve can be reduced to a geodesic curve giving the motion of a scalar test particle or/and a modified geodesic giving the motion of neutral spinning test particle in gravitational field. The new method used for derivation, the Bazanki method, shows a new feature in the new curve equation. This feature is that the equation contains the electromagnetic potential term together with the Lorentz term. We show the importance of this feature in physical applications.