Superintegrable families of magnetic monopoles with non-radial potential in curved background

TL;DR

This paper explores the superintegrability of magnetic monopole systems in curved backgrounds, extending known results from Euclidean space and Taub-NUT spaces, and introduces new findings on systems with non-radial potentials.

Contribution

It extends superintegrability results to curved spaces related to Taub-NUT via conformal transformations and presents new findings on minimal superintegrability with non-radial potentials.

Findings

Superintegrability extends to certain curved backgrounds.

Curvature depends on a rational parameter linked to integrals.

New results on minimal superintegrability with non-radial potentials.

Abstract

We review some known results on the superintegrability of monopole systems in the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT spaces. We show that these results can be extended to certain curved backgrounds that, for suitable choice of the domain of the coordinates, can be related via conformal transformations to systems in Taub-NUT spaces. These include the multi-fold Kepler systems as special cases. The curvature of the space is not constant and depends on a rational parameter that is also related to the order of the integrals. New results on minimal superintegrability when the electrostatic potential depends on both radial and angular variables are also presented.