RELATIVISTIC QUANTUM-MECHANICS OF THE ANYON

We quantize the effective action for a single relativistic anyon which is obtained by performing the path integral over the Abelian Chern-Simons gauge field in the theory where the anyon is described as a charged point particle coupled with the gauge field. identifying appropriately chosen Darboux variables of the Lorentz group in (2+1) dimensions with the canonical variables of the system, we show that the Hamiltonian only consists of two constraints corresponding to the mass shell condition and the Pauli-Lubanski equation. Thus. the effective action consistently describes a single free relativistic anyon whose wave function carries the unitary irreducible representation of the Poincare algebra.