Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

TL;DR

This paper constructs a three-dimensional ${ m N}=4$ supersymmetric mechanics with a Dirac monopole via Hamiltonian reduction from four-dimensional space, revealing a spin-orbit coupling term and providing explicit formulas.

Contribution

It introduces a novel Hamiltonian reduction approach to ${ m N}=4$ supersymmetric mechanics with monopoles, including explicit Hamiltonian and supercharges expressions.

Findings

The resulting system includes a magnetic monopole and spin-orbit coupling.

Explicit formulas for Hamiltonian and supercharges are provided.

Comparison with previous models highlights new features.

Abstract

We apply the technique of Hamiltonian reduction for the construction of three-dimensional ${\cal N}=4$ supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional ${\cal N}=4$ supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparison with previous work is also carried out.