CPN-1 MODELS AND THEIR NON-ABELIAN VERSION HPN-1 - STUDY OF THE QUANTUM PROPERTIES

A class of models with non-abelian gauge invariance called HPn-1 (they are a generalization of the abelian CPn-1 models) is considered at the quantum level, in particular in view of their relation with the O(n) non-linear σ-models, which is connected with the confinement property. Renormalization, critical behaviour and the 1 n expansion are studied in 2 or 2 + ε{lunate} dimensions. A comparison between the abelian CPn-1 and the non-abelian HPn-1 allows us to discuss the rôle of the classical solutions in the confinement problem. © 1979.