Monopole supersymmetries and the Biedenharn operator

TL;DR

This paper explores the hidden supersymmetry in monopole systems, extending previous work to spin-2 particles with additional potentials, and connects it to the Biedenharn operator, providing explicit solutions.

Contribution

It generalizes the monopole supersymmetry to higher spin particles with extra potentials and relates it to the Biedenharn operator, offering explicit solutions.

Findings

Identification of supersymmetry in spin-2 monopole systems

Connection between monopole supersymmetry and Biedenharn operator

Explicit solutions via diagonalization of the Biedenharn operator

Abstract

The hidden supersymmetry of the monopole found by De Jonghe et al. is generalized to a spin $\2$ particle in the combined field of a Dirac monopole plus a $\lambda^2/r^2$ potential [considered before by D'Hoker and Vinet], and related to the operator introduced by Biedenharn a long time ago in solving the Dirac-Coulomb problem. Explicit solutions are obtained by diagonalizing the Biedenharn operator