  We consider a neutral self-interacting massive scalar field defined in a
d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the
one-loop perturbative renormalization of this theory in the presence of rigid
boundary surfaces (two parallel hyperplanes), which break translational
symmetry. In order to identify the singular parts of the one-loop two-point and
four-point Schwinger functions, we use a combination of dimensional and
zeta-function analytic regularization procedures. The infinities which occur in
both the regularized one-loop two-point and four-point Schwinger functions fall
into two distinct classes: local divergences that could be renormalized with
the introduction of the usual bulk counterterms, and surface divergences that
demand countertems concentrated on the boundaries. We present the detailed form
of the surface divergences and discuss different strategies that one can assume
to solve the problem of the surface divergences. We also briefly mention how to
overcome the difficulties generated by infrared divergences in the case of
Neumann-Neumann boundary conditions.
