Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls

TL;DR

This paper develops simplified, numerically friendly formulas for calculating vacuum energy in static, radially symmetric backgrounds and domain walls, extending previous methods using zeta functions and Gel'fand-Yaglom theorem.

Contribution

It introduces new expressions for vacuum energy computation applicable to higher-dimensional radial systems and domain walls, enhancing numerical efficiency.

Findings

Derived new formulas for vacuum energy in radial backgrounds.

Extended zeta function and Gel'fand-Yaglom methods to higher dimensions.

Applicable to both zero and nonzero temperature scenarios.

Abstract

We extend our previous results of simplified expressions for functional determinants for radial Schr\"odinger operators to the computation of vacuum energy, or mass corrections, for static but spatially radial backgrounds, and for domain wall configurations. Our method is based on the zeta function approach to the Gel'fand-Yaglom theorem, suitably extended to higher dimensional systems on separable manifolds. We find new expressions that are easy to implement numerically, for both zero and nonzero temperature.