The Casimir energy for two-dimensional deformed sphere

TL;DR

This paper calculates the Casimir energy for a scalar field on a space combining flat dimensions with a deformed two-sphere, extending understanding of quantum vacuum effects in non-standard geometries.

Contribution

It introduces a method to compute Casimir energy on a space with a deformed two-sphere, a novel geometric setting.

Findings

Casimir energy depends on the deformation of the sphere.

Explicit formulas for the Casimir energy in this geometry are derived.

Results may impact quantum field theory in curved and deformed spaces.

Abstract

We compute the Casimir energy for a free scalar field on the spaces $\,R^{m+1}\,\times\,\tilde S^2\,$ where $,\tilde S^2\,$ is two-dimensional deformed two-sphere.