Semi-classical Dirac vacuum polarisation in a scalar field

TL;DR

This paper rigorously derives the semi-classical expansion of vacuum energy for a Dirac field coupled to a scalar, confirming classical formulas and exploring applications to large-coupling limits and system stability.

Contribution

It provides the first rigorous proof of the leading order vacuum energy expansion in a Dirac-scalar system and discusses its applications.

Findings

Rigorous proof of classical vacuum energy formula

Analysis of non-relativistic large-coupling limit

Insights into stability of homogeneous systems

Abstract

We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to Chin, Lee-Wick and Walecka, for which our result provides the first rigorous proof. We then discuss applications to the non-relativistic large-coupling limit of an interacting system, and to the stability of homogeneous systems.