### Abstract

We introduce an 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 the

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∗(R

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∗(R

^{1,2})×L^{1|1}. Where the Kähler supermanifold L^{1|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 L^{1|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 bosonic oscillator.Original language | English |
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Pages (from-to) | 3744-3755 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 56 |

DOIs | |

Publication status | Published - 1997 |

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## Cite this

Gorbunov, I. V., Kuzenko, S., & Lyakhovich, S. L. (1997). N=1, D = 3 superanyons, osp(2|2) and the deformed Heisenberg algebra.

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,*56*, 3744-3755. https://doi.org/10.1103/PhysRevD.56.3744