TOPOLOGY AND QUANTIZATION OF ABELIAN SIGMA-MODEL IN (1+1) DIMENSIONS

The abelian sigma model in (1 + 1) dimensions has a manifold-valued field phi: S-1 --> S-1. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that when a central extension is introduced into the algebra, the winding operator and the momenta operators satisfy anomalous commutators. We obtain an infinite number of inequivalent Hilbert spaces, which are characterized by a central extension and a continuous parameter alpha (0 less than or equal to alpha less than or equal to 1).