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 r : I → ℝ2k+1∖{0}, there is a 2-dimensional cone with vertex at the origin on which r is a geodesic.