Soliton operators in the quantum equivalence of the CP1 and O(3) - σmodels

Abstract

We discuss some interesting aspects of the well known quantum equivalence between the O(3) - σ and CP1 models in 3D, working inthe canonical and in the path integral formulations. We show first that the canonical quantization in the hamiltonian formulation is freeof ordering ambiguities for both models. We use the canonical map between the fields and momenta of the two models and compute therelevant functional determinant to verify the equivalence between the phase-space partition functions and the quantum equivalence in allthe topological sectors. We also use the explicit form of the map to construct the soliton operator of the O(3) - σ model starting from therepresentation of the operator in the CP1 model, and discuss their properties.