Inequivalent quantizations for non-linear σ model

Abstract

We compute the homotopy groups π₀ π₁ of the classical configuration space of an 0(3) invariant field theory on X×R, where X is a compact two dimensional manifold for arbitrary genusg and R denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications.