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.

8 pages. arXiv admin note: substantial text overlap with arXiv:1302.7271; text overlap with arXiv:1407.7919, arXiv:1211.5992 by other authors

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