On the nature of fermion-monopole supersymmetry

TL;DR

This paper reveals that the fermion-monopole system exhibits a nonlinear N=3/2 supersymmetry, which simplifies to a standard N=1 supersymmetry upon reduction to spherical geometry, providing new insights into its algebraic structure.

Contribution

It demonstrates that the fermion-monopole supersymmetry involves a product operator for independent supercharges and identifies a nonlinear N=3/2 supersymmetry structure.

Findings

The fermion-monopole system has a nonlinear N=3/2 supersymmetry.

Reduction to spherical geometry yields a standard N=1 supersymmetry.

Supercharges can be represented in a scalar form.

Abstract

It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De Jonghe, Macfarlane, Peeters and van Holten, and the generator of its standard N=1/2 supersymmetry have to be supplemented by their product operator to be treated as independent supercharge. As a result, the fermion-monopole system possesses the nonlinear N=3/2 supersymmetry having the nature of the 3D spin-1/2 free particle's supersymmetry generated by the supercharges represented in a scalar form. Analyzing the supercharges' structure, we trace how under reduction of the fermion-monopole system to the spherical geometry the nonlinear N=3/2 superalgebra comprising the Hamiltonian and the total angular momentum as even generators is transformed into the standard linear N=1 superalgebra with the Hamiltonian to be the unique even generator.