Note on Supersymmetric Mechanics with Spin–Orbit Interaction

We propose a simple model of two-dimensional $$\mathcal{N} = 2$$ 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 $$\mathcal{N} = 4$$ superconformal mechanics $$D(1,2{\kern 1pt} |{\kern 1pt} \alpha )$$ . The bosonic part of the Hamiltonian describes a free particle on the cone, while the fermionic part necessarily includes the spin–orbit interaction term.