The Covariant Electromagnetic Casimir Effect for Real Conducting Cylindrical Shells

TL;DR

This paper calculates the electromagnetic Casimir force on real conducting cylindrical shells using covariant quantization, considering both boundary conditions and real material properties, with specific results for gold and silver shells.

Contribution

It introduces a covariant quantization approach for the Casimir effect on cylindrical shells with real conductors, incorporating plasma cut-off for renormalization.

Findings

Casimir pressure for gold and silver shells computed

Dirichlet and Neumann boundary conditions treated separately

Method accounts for real material properties

Abstract

Using covariant quantization of the electromagnetic field, the Casimir force per unit area experienced by a long conducting cylindrical shell, under both Dirichlet and Neumann boundary conditions, is calculated. The renormalization procedure is based on the plasma cut-off frequency for real conductors. The real case of a gold (silver) cylindrical shell is considered and the corresponding electromagnetic Casimir pressure is computed. It is discussed that the Dirichlet and Neumann problems should be considered separately without adding their corresponding results.