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

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.