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We introduce N=1 supersymmetric generalization of the mechanical systemdescribing a particle with fractional spin in D=1+2 dimensions and beingclassically equivalent to the formulation based on the Dirac monopole two-form.The model introduced possesses hidden invariance under N=2 Poincar\'esupergroup with a central charge saturating the BPS bound. At the classicallevel the model admits a Hamiltonian formulation with two first classconstraints on the phase space $T^*(R^{1,2})\times {\cal L}^{1|1}$, where theK\"ahler supermanifold ${\cal L}^{1|1}\cong OSp(2|2)/U(1|1)$ is a minimalsuperextension of the Lobachevsky plane. The model is quantized by combiningthe geometric quantization on ${\cal L}^{1|1}$ and the Dirac quantization withrespect to the first class constraints. The constructed quantum theorydescribes a supersymmetric doublet of fractional spin particles. The space ofquantum superparticle states with a fixed momentum is embedded into the Fockspace of a deformed harmonic oscillator.Comment: 23 pages, Late

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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N=1,D=3superanyons,osp(2|2), and the deformed Heisenberg …