Born-Oppenheimer Type Approximation for a Simple Renormalizable System

Abstract

We discuss a simple singular system in two dimension, two heavy particles interacting with a light particle via an attractive contact interaction. Although intuitively clear the actual application of the Born-Oppenheimer type approximation to this problem is quite subtle. The light particle ground state energy is not bounded from below when we consider it as a function of heavy particles’ separation. Nevertheless, with due care, we calculate the leading term of the Born-Oppenheimer type approximation and indicate how to get the higher order corrections.