Vacuum energy of a massive scalar field in the presence of a semi-transparent cylinder

TL;DR

This paper calculates the vacuum energy of a massive scalar field around a semi-transparent cylindrical shell, revealing that the energy can be negative for both attractive and repulsive potentials, using scattering theory and heat kernel methods.

Contribution

It introduces a method to compute the ground state energy of a scalar field with a delta-function potential on a cylindrical shell, combining scattering theory with heat kernel renormalization.

Findings

Vacuum energy is negative for both attractive and repulsive potentials.

The energy is expressed via the Jost function of the scattering problem.

Renormalization is performed using heat kernel expansion.

Abstract

We compute the ground state energy of a massive scalar field in the background of a cylindrical shell whose potential is given by a delta function. The zero point energy is expressed in terms of the Jost function of the related scattering problem, the renormalization is performed with the help of the heat kernel expansion. The energy is found to be negative for attractive and for repulsive backgrounds as well.