Abstract
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.
