Casimir Effect For a Scalar Field via Krein Quantization

TL;DR

This paper introduces a simplified method using Krein quantization to analyze the Casimir effect for a massless scalar field with Dirichlet boundary conditions on a spherical shell, offering a novel approach to renormalization.

Contribution

It applies Krein quantization to compute the Casimir effect, providing a new, straightforward technique for handling boundary conditions and renormalization in scalar field theories.

Findings

Successfully computes Casimir energy using Krein quantization.

Demonstrates the method's simplicity compared to traditional approaches.

Provides a framework for future studies of quantum field effects with boundary conditions.

Abstract

In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions.