The range of validity of strong and weak coupling approaches in field theory

Abstract

The solutions of scalar meson theory with infinitely heavy nucleons are well known in the limits of weak and strong coupling, and also there is the intermediate coupling method of Tomonaga which bridges the gap between them. However, the latter requires special trial functions and a cut-off procedure, so it is interesting to try to construct a method which develops a general solution analytically, particularly in order to answer the following question: When infinite quantities are absorbed by renormalization does the weakness or strongness of the coupling depend upon the renormalized quantities only? In this paper the problem of one nucleon is tackled in the functional integration formalism. It has been shown that this method encompasses both strong and weak limits, and here an attempt will be made to develop a general solution using the method of stationary phase.