Exactly renormalizable model in quantum field theory. I. The diagram analysis

Abstract

A simple model is considered for the interaction of a boson field with infinitely heavy nucleons, susceptible of an exact determination of the physical nucleon states and of the renormalization constants. The model is an extension of the Lee model as well as of the neutral scalar field in scalar interaction with heavy nucleons. The diagram analysis of the S-matrix and of the renormalization is carried out. The renormalized coupling constants remain different from zero for infinite cut-off. In this limit the theory becomes essentially equivalent to the neutral scalar field in interaction with heavy nucleons; it then gives vanishing boson-nucleon scattering but non-vanishing nucleon-nucleon interaction, the latter in contrast to the Lee model.