  An analysis of the one-loop vacuum fluctuations associated with a scalar
field confined in the interior of a infinite waveguide of rectangular cross
section is presented. We first consider the massless scalar field defined in a
four-dimensional Euclidean space. To identify the infinities of the vacuum
fluctuations we use a combination of dimensinal and zeta function analytic
regularization procedures. The infinities which occur in the one-loop vacuum
fluctuations fall into two distinct classes: ultraviolet divergences that are
renormalized by the introduction of bulk counterterms and also surface and
edges divergences that demand countertems concentrated on the boundaries. We
present the detailed form of the surface and edge divergences. Finally we
discuss how to generalize our calculations for a confined massive scalar field
defined in a higher dimensional Euclidean space.
