  The Schr\"odinger functional in Wilson's lattice QCD leads to a sensible
classical continuum theory which can be taken as starting point for a
perturbative analysis. In dimensional regularization, the saddle point
expansion of the Schr\"odinger functional is performed to one-loop order of
perturbation theory. The divergences are partly cancelled by the usual coupling
constant and quark mass renormalization. An additional divergence can be
absorbed in a multiplicative renormalization of the quark boundary fields. The
corresponding boundary counterterm being a local polynomial in the fields we
confirm the general expectation expressed by Symanzik~\cite{Symanzik}.
