Born-Oppenheimer Approximation for a Simple Renormalizable System

TL;DR

This paper demonstrates how to apply the Born-Oppenheimer approximation to a two-dimensional singular system with two heavy and one light particle, providing leading order calculations and guidance for higher order corrections.

Contribution

It presents a careful application of the Born-Oppenheimer approximation to a simple, yet subtle, two-dimensional singular system, including leading order results and correction methods.

Findings

Successfully applied Born-Oppenheimer approximation to the system

Calculated the leading term of the approximation

Outlined how to obtain higher order corrections

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 approximation to this problem is quite subtle. Nevertheless, with due care we show that this can be done, as a result we calculate the leading term of the Born-Oppenheimer approximation and indicate how to get the higher order corrections.