Vacuum energy in a spherically symmetric background field

TL;DR

This paper calculates the vacuum energy of a scalar field in a spherically symmetric background using scattering theory, discusses renormalization, and demonstrates the method with an explicit example.

Contribution

It introduces a method to compute vacuum energy via the Jost function and details the renormalization process in this context.

Findings

Vacuum energy expressed through the Jost function.

Renormalization performed using uniform asymptotic expansion.

Method demonstrated with a simple explicit example.

Abstract

The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in a simple explicit example.