N=1, D=3 superanyons, osp(22), and the deformed Heisenberg algebra
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 twoform. 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^{1,2})×L^{11}, where the Kähler supermanifold L^{11}≅OSp(22)/U(11) is a minimal superextension of the Lobachevsky plane. The model is quantized by combining the geometric quantization on L^{11} 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.
 Publication:

Physical Review D
 Pub Date:
 September 1997
 DOI:
 10.1103/PhysRevD.56.3744
 arXiv:
 arXiv:hepth/9702017
 Bibcode:
 1997PhRvD..56.3744G
 Keywords:

 11.30.Pb;
 71.10.Pm;
 Supersymmetry;
 Fermions in reduced dimensions;
 High Energy Physics  Theory
 EPrint:
 23 pages, Latex