GAUGE-INDEPENDENT ANALYSIS OF O(3) NONLINEAR SIGMA-MODEL WITH HOPF AND CHERN-SIMONS TERMS

The (2 + 1)-dimensional nonlinear sigma model with a Hopf term (Wilczek-Zee model) is generalised to include a Chem-Simons three-form. Contrary to the Wilczek-Zee model, this model turns out to be a local gauge theory. It is quantised in the hamiltonian (Dirac) formalism without gauge fixing. Poincare covariance of the theory is established, and subtleties related to the structure of different (canonical or symmetric) forms of the energy-momentum tensor are illuminated. The role of constraints and gauge invariance in the analysis is emphasised. Advantages of our gauge-independent formalism compared with usual gauge-fixed approaches are illustrated. The differences, at the conceptual and technical levels, between the usual Wilczek-Zee model and that treated here are highlighted both in the canonical and path-integral formalisms. The angular-momentum operator is analysed, and the conventional result connecting the topological charge with the ''fractional spin'' is elaborated.