Radiative Corrections to Casimir Effect in the $\lambda\phi^{4}$ Model

TL;DR

This paper computes the quantum radiative corrections to the Casimir effect for a massive complex scalar field with self-interaction, considering various boundary conditions in higher-dimensional spacetime.

Contribution

It provides the first detailed calculation of radiative corrections to the Casimir effect for the $ ext{lambda}\phi^4$ model under multiple boundary conditions in arbitrary dimensions.

Findings

Radiative corrections depend on boundary conditions and dimensionality.

Quasi-periodic boundary conditions interpolate between periodic and anti-periodic cases.

Results extend understanding of quantum effects in confined scalar fields.

Abstract

We calculate radiative corrections to the Casimir effect for the massive complex scalar field with the $\lambda\phi^{4}$ self-interaction in $d+1$ dimensions. We consider the field submitted to four types of boundary conditions on two parallel planes, namely: (i) quasi-periodic boundary conditions, which interpolates continuously periodic and anti-periodic ones, (ii) Dirichlet conditions on both planes, (iii) Neumann conditions on both planes and (iv) mixed conditions, that is, Dirichlet on one plane and Neumann on the other one.