Quantization ambiguity and non-trivial vacuum structure

Abstract

It is pointed out that there is an ambiguity in quantization of any system whose configuration space has a non-trivial topology characterized by a Chern number. In field theories this ambiguity manifests itself through the existence of θ sectors. The point of view adopted gives a simple interpretation of the difference between the temporal and Coulomb gauge descriptions of instantons. The general ideas are exemplified in the O(3) non-linear σ model in two dimensions.