Functional determinants and Casimir energy in higher dimensional spherically symmetric background potentials

TL;DR

This paper develops a method to compute the spectral zeta function for Laplace operators in higher dimensions with spherical symmetry, enabling straightforward calculation of functional determinants and Casimir energies.

Contribution

It introduces a novel analytic continuation technique for the spectral zeta function in higher-dimensional spherically symmetric backgrounds, simplifying the evaluation of physical quantities.

Findings

Derived explicit formulas for functional determinants.

Calculated Casimir energies in higher-dimensional spherical backgrounds.

Provided a new approach for spectral zeta function analysis.

Abstract

In this paper we analyze the spectral zeta function associated with a Laplace operator acting on scalar functions on an N-dimensional Euclidean space in the presence of a spherically symmetric background potential. The obtained analytic continuation of the spectral zeta function is then used to derive very simple results for the functional determinant of the operator and the Casimir energy of the scalar field.