Radiative corrections to the Casimir effect for the massive scalar field

TL;DR

This paper calculates the first-order radiative correction to the Casimir energy for a massive scalar field with different boundary conditions, revealing boundary sensitivity except in the massless limit.

Contribution

It provides the first explicit computation of the $O(\lambda)$ correction for the massive scalar Casimir effect under Dirichlet and Neumann conditions.

Findings

Correction depends on boundary conditions for finite mass.

Results agree with existing literature in the zero mass limit.

Boundary sensitivity diminishes as mass approaches zero.

Abstract

We compute the $O(\lambda)$ correction to the Casimir energy for the massive $\lambda\phi^4$ model confined between a pair of parallel plates. The calculations are made with Dirichlet and Neumann boundary conditions. The correction is shown to be sensitive to the boundary conditions, except in the zero mass limit, in which case our results agree with those found in the literature.