Krein Space Quantization of Casimir Effect for a Spherical Shell

F Payandeh

doi:10.5402/2012/714823

Abstract

The Casimir stress on a spherical shell in de Sitter spacetime for a massless scalar field is calculated using Krein space quantization. In this method, the auxiliary negative frequency states have been utilized, the modes of which do not interact with the physical states and are not affected by the physical boundary conditions. These unphysical states just play the role of an automatic renormalization tool for the theory.

Highlights

The Casimir effect is a small attractive force acting between two parallel uncharged conducting plates and it is regarded as one of the most striking manifestation of vacuum fluctuations in quantum field theory
The particular features of these forces depend on the nature of the quantum field, the type of spacetime manifold and its dimensionality, the boundary geometries, and the specific boundary conditions imposed on the field
ISRN High Energy Physics the Casimir effect has been calculated for a massless scalar field satisfying Dirichlet boundary conditions on the spherical shell in de Sitter space

Summary

Introduction

The Casimir effect is a small attractive force acting between two parallel uncharged conducting plates and it is regarded as one of the most striking manifestation of vacuum fluctuations in quantum field theory. ISRN High Energy Physics the Casimir effect has been calculated for a massless scalar field satisfying Dirichlet boundary conditions on the spherical shell in de Sitter space. It has been shown that the linear quantum gravity in the background field method is perturbatively nonrenormalizable and there appears an infrared divergence This infrared divergence does not manifest itself in the quadratic part of the effective action in the one-loop approximation. It has been proved that the use of the two sets of solutions positive and negative norm states is an unavoidable feature if one wants to preserve causality locality , covariance, and elimination of the infrared divergence in quantum field theory for the minimally coupled scalar field in de Sitter space 29, 30 , that is, Krein space quantization. Applying the unphysical negative frequency states and defining the field operator in Krein space, we can calculate the gravitational pressure on a spherical shell yielding the standard result obtained

Scalar Casimir Effect for a Sphere in de Sitter Space

Spherical Shell with Different Vacua in Krein Space Quantization

Conclusion