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

I.V Gorbunov, Sergei Kuzenko, S.L. Lyakhovich

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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∗(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 bosonic oscillator.
Original languageEnglish
Pages (from-to)3744-3755
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Publication statusPublished - 1997


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