Exactly renormalizable model in the quantum theory of fields

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. It incorporates as special cases the Lee model and the neutral scalar field in scalar interaction with heavy nucleons. The renormalized coupling constants remain different from zero for infinite cut-off although part of the physical effects of the coupling vanish in this limit. The system becomes then essentially equivalent to the neutral scalar field in scalar interaction with heavy nucleons, which gives vanishing boson-nucleon scattering but non-vanishing nucleon-nucleon interaction.