Topology and quantization of abelian sigma model in (1+1) dimensions

Abstract

The abelian sigma model in (1+1) dimensions has a manifold-valued field φ: 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 α (0≤ α<1).