MICZ-Kepler = dynamics on the cone over the rotation group

TL;DR

This paper demonstrates that the n-dimensional MICZ-Kepler system can be derived from symplectic reduction of a mechanical system on a cone over SO(n), providing a new geometric perspective and an explicit solution formula.

Contribution

It reveals the geometric origin of the MICZ-Kepler system as a reduction on a cone over the rotation group and derives an explicit solution formula.

Findings

MICZ-Kepler system arises from symplectic reduction on a cone

Derived an explicit formula for the general solution

Identified the potential term as part of the cone's kinetic energy

Abstract

We show that the n-dimensional MICZ-Kepler system arises from symplectic reduction of a simple mechanical system on the cone over the rotation group SO(n). As a corollary we derive an elementary formula for its general solution. The punch-line of our computation is that the additional MICZ-Kepler $|\phi|^2/r^2$ type potential term is the rotational part of the cone's kinetic energy.