A functional approach to the Van der Waals interaction

TL;DR

This paper develops a microscopic, functional integral approach to derive the Van der Waals interaction energy between neutral atoms, capturing both weak and strong coupling regimes and their physical implications.

Contribution

It introduces a novel functional integral framework to evaluate atomic Van der Waals forces from a microscopic model, including strong-coupling effects and potential vacuum decay.

Findings

Derived the Van der Waals energy at first order in fine structure constant

Explored the strong-coupling limit revealing vacuum decay thresholds

Analyzed effects of general central potentials on interactions

Abstract

Based on a microscopic model, we use a functional integral approach to evaluate the quantum interaction energy between two neutral atoms. Each atom is coupled to the electromagnetic (EM) field via a dipole term, generated by an electron bound to the nucleus via a harmonic potential. We show that the resulting expression for the energy becomes the Van der Waals interaction energy at the first non-trivial order in an expansion in powers of the fine structure constant, encompassing both the long and short distance behaviours. We also explore the opposite, strong-coupling limit, which yields a result for the interaction energy as well as a threshold for the existence of a vacuum decay probability, manifested here as an imaginary part for the effective action. In the weak-coupling limit, we also study the effect of using a general central potential for the internal structure of the atoms.