Energy of the vacuum with a perfectly conducting and infinite cylindrical surface

TL;DR

This paper calculates the vacuum energy of scalar fields around an infinite cylindrical surface using zeta function regularization, confirming previous electromagnetic Casimir effect results and highlighting boundary condition effects.

Contribution

It introduces a complete zeta function regularization scheme for scalar fields with boundary conditions on a cylindrical surface, advancing the theoretical understanding of vacuum energies.

Findings

Vacuum energies for scalar fields are of opposite signs under different boundary conditions.

The study confirms the electromagnetic Casimir effect in cylindrical geometries.

A new regularization approach improves the calculation accuracy.

Abstract

Values for the vacuum energy of scalar fields under Dirichlet and Neuman boundary conditions on an infinite clylindrical surface are found, and they happen to be of opposite signs. In contrast with classical works, a complete zeta function regularization scheme is here applied. These fields are regarded as interesting both by themselves and as the key to describing the electromagnetic (e.m.) case. With their help, the figure for the e.m. Casimir effect in the presence of this surface, found by De Raad and Milton, is now confirmed.