  The quantisation of a scalar field in the five-dimensional model suggested by
Randall and Sundrum is considered. Using the Kaluza-Klein reduction of the
scalar field, discussed by Goldberger and Wise, we sum the infinite tower of
modes to find the vacuum energy density. Dimensional regularisation is used and
we compute the pole term needed for renormalisation, as well as the finite part
of the energy density. Some comments are made concerning the possible
self-consistent determination of the radius.
