Radiative corrections to the Casimir effect for the massive scalar field

TL;DR

This paper calculates the first radiative correction to the Casimir energy for a massive scalar field with self-interaction between parallel plates, considering different boundary conditions using regularization techniques.

Contribution

It provides a novel calculation of radiative corrections to the Casimir effect for a massive scalar field with various boundary conditions.

Findings

Radiative corrections depend on boundary conditions.

Results obtained using dimensional and analytical regularizations.

First such correction computed for a massive scalar field with self-interaction.

Abstract

We compute the first radiative correction to the Casimir energy of a massive scalar field with a quartic self-interaction in the presence of two parallel plates. Three kinds of boundary conditions are considered: Dirichlet-Dirichlet, Neumann-Neumann and Dirichlet-Neumann. We use dimensional and analytical regularizations to obtain our physical results.