Quantised bulk fields in the Randall–Sundrum compactification model

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.