Renormalization Group Functions of CPN-1 Non-Linear  -Model and N-Component Scalar QED Model

Abstract

The renormalization group functions of CPN-I non-linear O"-model are studied in 2+< dimension by the 365. By the 1/ N-expansion, the relation of CPN-1 model and scalar QED model will be studied. In the statistical mechanics, the superconductor phase transition or smectic A~nematic phase transition may be formulated by the scalar QED model. This problem is also discussed in this paper. *1 We note a complex projection-SU(N) model by the CPN-I model. **l The generalization of this cpN-I model to the non-abelian case has been studied in 2+ E dimension by Bn~zin, Hikami and Zinn-Justin (to be published) including this cpN-I model.