Deformed supersymmetric quantum mechanics with spin variables

Abstract We quantize the one-particle model of the SU(2|1) supersymmetric multiparticle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter m and SU(2) spin q∈ℤ>0,1/2+ℤ≥0 $$ q\in \left({\mathrm{\mathbb{Z}}}_{>0,}1/2+{\mathrm{\mathbb{Z}}}_{\ge 0}\right) $$. It is found that the states at the fixed energy level form irreducible multiplets of the supergroup SU(2|1). Also, the hidden superconformal symmetry OSp(4|2) of the model is revealed in the classical and quantum cases. We calculate the OSp(4|2) Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed q are unified into an irreducible OSp(4|2) multiplet