Casimir Effect of Scalar Massive Field

TL;DR

This paper derives a formalism to calculate the Casimir force for a massive scalar field, relating it to Green functions and extending the analysis to higher-dimensional spacetimes.

Contribution

It introduces a novel approach to evaluate the Casimir force using Green functions and fluctuation-dissipation theorem, avoiding explicit field quantization.

Findings

Derived expressions for Casimir force using Green functions.

Extended formalism to D+1 dimensions.

Calculated attractive force between plates.

Abstract

The energy momentum tensor is used to introduce the Casimir force of the massive scalar field acting on a nonpenetrating surface. This expression can be used to evaluate the vacuum force by employing the appropriate field operators. To simplify our formalism we also relates the vacuum force expression to the imaginary part of the Green function via the fluctuation dissipation theorem and Kubo formula. This allows one to evaluate the vacuum force without resorting to the process of field quantization. These two approaches are used to calculate the attractive force between two nonpenetrating plates. Special attention is paid to the generalization of the formalism to D + 1 space-time dimensions.