HOPF TERM, FRACTIONAL SPIN AND SOLITON OPERATORS IN THE O(3) NONLINEAR SIGMA-MODEL

We re-examine three issues, the Hopf term, fractional spin and the sol iton operators, in the 2 + 1 dimensional O(3) non-linear sigma model b ased on the adjoint orbit parametrization (AOP) introduced earlier. It is shown that the Hopf term is well defined for configurations of any soliton charge Q if we adopt a time-independent boundary condition at spatial infinity. We then develop the Hamiltonian formulation of the model in the AOP and thereby argue that the well-known Q(2) formula fo r fractional spin holds only for a restricted class of configurations. Operators that create states of given classical configurations of any soliton number in the (physical) Hilbert space are constructed. Our r esults clarify some of the points that are crucial for the above three topological issues and yet have remained obscure in the literature. ( C) 1998 Elsevier Science B.V.