, D = 3 Superanyons , osp ( 2 | 2 ) and the Deformed Heisenberg Algebra

We introduce N = 1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D = 1 + 2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model introduced possesses hidden invariance under N = 2 Poincaré supergroup with a central charge saturating the BPS bound. At the classical level the model admits a Hamiltonian formulation with two first class constraints on the phase space T ∗(R1,2)×L1|1, where the Kähler supermanifold L1|1 ∼= OSp(2|2)/U(1|1) is a minimal superextension of the Lobachevsky plane. The model is quantized by combining the geometric quantization on L1|1 and the Dirac quantization with respect to the first class constraints. The constructed quantum theory describes a supersymmetric doublet of fractional spin particles. The space of quantum superparticle states with a fixed momentum is embedded into the Fock space of a deformed harmonic oscillator.