Calculating Vacuum Energies in Quantum Field Theory

TL;DR

This paper introduces an efficient method for calculating vacuum energies in quantum field theory using scattering data and Green's functions, simplifying renormalization and enabling practical computations in Casimir problems.

Contribution

It presents a novel approach leveraging scattering data and Green's functions to compute vacuum energies, streamlining renormalization in quantum field theory.

Findings

Efficient computation of vacuum energies using Green's functions.

Simplified renormalization process via Born approximation.

Numerical examples demonstrating method's effectiveness.

Abstract

A new approach to generalised Casimir type of problems is derived within the context of renormalisable quantum field theory (QFT). We study the simplest case of a massive fluctuating boson field coupled to a time-independent background potential. We use analytic properties of scattering data to compute the relevant Green's functions at imaginary momenta, which in turn yields a simple and efficient method to compute (one-loop) vacuum energy densities in QFT. Renormalisation is easily performed in the perturbative sector by identifying low order Feynman diagrams with the first few Born approximation to the Green's function. Numerical examples illustrate the efficiency of our approach.