Equivalence of model space techniques and the renormalization group for a separable model problem

Abstract

Lee–Suzuki similarity transformations and Krenciglowa–Kuo folded diagrams are two common methods used to derive energy independent model space effective interactions for nuclear many-body systems. We demonstrate that these two methods are equivalent to a Renormalization Group (RG) analysis of a well-studied problem in quantum mechanics. The effective low-momentum potentials V eff obtained from model space methods are shown to obey the same scaling equation for V eff that RG arguments predict. This indicates that model space methods might be of interest to those studying low-energy nuclear physics using Effective Field Theories (EFT). We find the new result that all of the different energy independent model space techniques yield a unique low-momentum V eff when applied to the toy model under consideration.