Casimir Pistons for Massive Scalar Fields

TL;DR

This paper calculates the Casimir force on two-dimensional pistons for massive scalar fields with various boundary conditions, analyzing the effects of mass and position, and comparing to massless cases using zeta-function regularization.

Contribution

It introduces a generalized zeta-function regularization approach to compute Casimir forces for massive scalar fields with different boundary conditions.

Findings

Casimir force depends on mass and piston position

Force behavior differs between Dirichlet and hybrid boundary conditions

Comparison shows differences between massive and massless scalar fields

Abstract

The Casimir force on two-dimensional pistons for massive scalar fields with both Dirichlet and hybrid boundary conditions is computed. The physical result is obtained by making use of generalized $\zeta$-function regularization technique. The influence of the mass and the position of the piston in the force is studied graphically. The Casimir force for massive scalar field is compared to that for massless scalar field.