New Supersymmetry of the Monopole

TL;DR

This paper reveals a new supersymmetry in the non-relativistic spin-1/2 particle dynamics in a monopole field, expanding understanding of the system's symmetry structure and its geometric origins.

Contribution

It identifies and explains a novel supersymmetry that squares to the rotation group's Casimir invariant, complementing previously known supersymmetries in monopole systems.

Findings

Discovery of a new supersymmetry in monopole dynamics

Connection between supersymmetry and geometry of spinning particles on a sphere

Enhanced symmetry understanding of monopole-related quantum systems

Abstract

The non-relativistic dynamics of a spin-1/2 particle in a monopole field possesses a rich supersymmetry structure. One supersymmetry, uncovered by d'Hoker and Vinet, is of the standard type: it squares to the Hamiltonian. In this paper we show the presence of another supersymmetry which squares to the Casimir invariant of the full rotation group. The geometrical origin of this supersymmetry is traced, and its relationship with the constrained dynamics of a spinning particle on a sphere centered at the monopole is described.