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

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.