Note on supersymmetric mechanics with spin-orbit interaction

Abstract

We propose a simple model of two-dimensional N=2 superconformal mechanics with a spin-orbit interaction term and demonstrate that it inherits the Galilean symmetry of the initial free-particle system. We then propose a quaternionic counterpart of this system, which describes the four-dimensional N=4 superconformal mechanics$D(1,2|\alpha). The bosonic part of the Hamiltonian describes a free particle on the cone, while the fermionic part necessarily includes the spin-orbit interaction term.