QUANTUM MECHANICALLY INDUCED HOPF TERM IN THE O(3) NONLINEAR SIGMA-MODEL

The Hopf term in the (2 + 1)-dimensional O(3) nonlinear sigma model, w hich is known to be responsible for fractional spin and statistics, is re-examined from the viewpoint of quantization ambiguity. It is confi rmed that the Hopf term can be understood as a term induced quantum me chanically, in precisely the same manner as the theta-term in QCD, We present a detailed analysis of the topological aspect of the model bas ed on the adjoint orbit parametrization of the spin vectors, which is not only very useful in handling topological (soliton and/or Hopf) num bers, but also plays a crucial role in defining the Hopf term for conf igurations of nonvanishing soliton numbers. The Hopf term is seen to a rise explicitly as a quantum effect which emerges when quantizing an S -1 degree of freedom hidden in the configuration space. (C) 1998 Elsev ier Science B.V.