Mass renormalization and binding energies in quantum field theory

Abstract

We compare the predictions of two methods of determining the amount of binding energy between two distinguishable fermions that interact with each other through force-intermediating bosons. Both measures try to quantify this binding energy by the downward shift of the fully interacting two-fermion ground state energy relative to the sum of the corresponding two single-particle ground state energies. The first method computes this energy difference directly from the standard quantum field theoretical Hamiltonian. The second method uses the mass renormalized form of this Hamiltonian. In order to have a concrete example for this comparison, we employ a simple Yukawa-like model system in one spatial dimension. We find that both approaches lead to identical predictions in the second and fourth order perturbation of the coupling constant, and they remain remarkably close even in the strong coupling domain where perturbation theory diverges. This illustrates that there are field theoretical systems for which rather accurate binding energies can be obtained even without the mass renormalization procedure.