Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole

Understand

We propose Lagrangian and Hamiltonian formulations of a N=4 supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific scalar potential.

• This additional potential is completely fixed by N=4 supersymmetry and in the simplest case of flat metrics it coincides with that which provides the existence of the Runge-Lenz vector for the bosonic subsector.
• The isospin degrees of freedom are described on the Lagrangian level by bosonic auxiliary variables forming N=4 supermultiplet with additional, also auxiliary fermions.
• Being quite general, the constructed systems include such interesting cases as N=4 superconformally invariant systems with Wu-Yang monopole, the particles living in the flat R^3 and in the R x S^2 spaces and interacting with the monopole, and also the particles moving on three-dimensional sphere and pseudo-sphere with Wu-Yang monopole sitting in the center.