Particle Motion in Generalized Dirac's Monopoles of dimension 2k+1

TL;DR

This paper derives the equations of motion for a charged particle in a generalized Dirac monopole field in odd-dimensional Euclidean spaces, revealing that particle trajectories lie on specific 2D cones as geodesics.

Contribution

It extends Meng's ideas to formulate particle motion equations in higher-dimensional monopole fields, showing trajectories are confined to 2D cones as geodesics.

Findings

Particle trajectories lie on 2D cones centered at the origin.

Trajectories are geodesics on these cones.

Generalization to odd-dimensional Euclidean spaces.

Abstract

By using Meng's idea in his generalization of the classical MICZ-Kepler problem, we obtained the equations of motion of a charged particle in the field of generalized Dirac monopole in odd dimensional Euclidean spaces. The main result is that for every particle trajectory $\mathbf{r}: I\to\mathbb{R}^{2k+1} \setminus \{0\}$, there is a 2-dimensional cone with vertex at the origin on which $\mathbf{r}$ is a~geodesic.