Multi-center MICZ-Kepler system, supersymmetry and integrability

TL;DR

This paper introduces a general framework for integrating Dirac monopoles into three-dimensional conformal flat space mechanical systems, extending known integrable systems like the MICZ-Kepler model, and explores their supersymmetry and integrability properties.

Contribution

It develops a universal scheme to incorporate Dirac monopoles into existing integrable systems, broadening the class of solvable models in mathematical physics.

Findings

Extended systems admit separation of variables in elliptic or parabolic coordinates.

Constructed multi-center MICZ-Kepler systems with monopoles at coordinate foci.

Identified specific physical models, including quantum dots with external fields.

Abstract

We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic or parabolic coordinates can be extended to the integrable system with the Dirac monopoles located at the foci of the corresponding coordinate systems. Particular cases of this class of system are the two-center MICZ-Kepler system in the Euclidean space, the limiting case when one of the background dyons is located at the infinity as well as the model of particle in parabolic quantum dot in the presence of parallel constant uniform electric and magnetic fields.