Magnetic monopoles and dyons revisited: A useful contribution to the study of classical mechanics

TL;DR

This paper revisits the classical mechanics problem of magnetic monopoles and dyons, demonstrating their unique properties and pedagogical value, including stable non-planar orbits and rainbow scattering, extending traditional Kepler problem concepts.

Contribution

It introduces a classical mechanics analysis of dyon interactions, expanding educational examples beyond the Kepler problem and Rutherford scattering with novel properties.

Findings

Stable non-planar orbits observed

Rainbow and glory scattering phenomena identified

Extension to relativistic and semi-classical quantization possible

Abstract

Graduate level physics curricula in many countries around the world, as well as senior-level undergraduate ones in some major institutions, include Classical Mechanics courses, mostly based on Goldstein's textbook masterpiece. During the discussion of central force motion, however, the Kepler problem is virtually the only serious application presented. In this paper, we present another problem that is also soluble, namely the interaction of Schwinger's dual-charged (dyon) particles. While the electromagnetic interaction of magnetic monopoles and electric charges was studied in detail some 40 years ago, we consider that a pedagogical discussion of it from an essentially classical mechanics point of view is a useful contribution for students. Following a path that generalizes Kepler's problem and Rutherford scattering, we show that they exhibit remarkable properties such as stable non-planar orbits, as well as rainbow and glory scattering, which are not present in the ordinary scattering of two singly charged particles. Moreover, it can be extended further to the relativistic case and to a semi-classical quantization, which can also be included in the class discussion.