Zeta function for perturbed surfaces of revolution

TL;DR

This paper investigates how small perturbations on surfaces of revolution affect the Zeta function, the functional determinant, and the Casimir energy, providing insights into quantum field effects on perturbed geometries.

Contribution

It introduces a novel analysis of the Zeta function for perturbed surfaces of revolution and examines the impact on physical quantities like Casimir energy.

Findings

Perturbations alter the Zeta function and functional determinant.

Changes in Casimir energy are quantified for perturbed geometries.

Provides a framework for analyzing quantum effects on deformed surfaces.

Abstract

In this paper we explore the Zeta function arising from a small perturbation on a surface of revolution and the effect of this on the functional determinant and in the change of the Casimir energy associated with this configuration.