A new proof of the asymptotic nature of perturbation theory in P(phi)2 models

A new method of proving the asymptotic nature of perturbation theory (for Schwinger and generalized Schwinger functions) in P(phi)2 quantum field models, which does not presume the convergence of a cluster expansion, is presented. The method recaptures all previous such results and, also, results (in application to certain models [Su 1,2]) not yet attainable by previous methods. An explicit proof is given for (phi4)2 in the two phase region to illustrate the essential points. Application to all P(phi)2 models with mean field limits is discussed. (Auth.)