Scaling limit for the Derezi\'nski-G\'erard model

Abstract

We consider a scaling limit for the Derezi\'nski-G\'erard model. We derive an effective potential by taking a scaling limit for the total Hamiltonian of the Derezi\'nski-G\'erard model. Our method to derive an effective potential is independent of whether or not the quantum field has a nonnegative mass. As an application of our theory developed in the present paper, we derive an effective potential of the Nelson model.