Renarks on the classical limit of quantum field theories

Recently, there has been an increasing interest in computing quantum mechanical corrections to solutions of classical field equations. In this note, we want to proceed in the opposite way and we summarize theorems about the classical limit of relativistic quantum field models. These results are a byproduct of the so called constructive approach to quantum field theory.After a section on generalities, we discuss in Section 2 the situation where no phase transitions occur in the limith0 and in Section 3 we reformulate one result in the case where such a transition occurs (Glimmet al. 7]). We discuss the validity of the loop expansion. It seems however that the tools to show the rigorous validity of soliton calculations are not yet prepared.