THE RUNNING COUPLING FROM THE QCD SCHRODINGER FUNCTIONAL - A ONE-LOOPANALYSIS

Starting from the Schrodinger functional, we give a non-perturbative d efinition of the running coupling constant in QCD. The spatial boundar y conditions for the quark fields are chosen such that the massless Di rac operator in the classical background field has a large smallest ei genvalue. At one-loop order of perturbation theory, we determine the m atching coefficient to the <(MS)over bar> scheme and discuss the quark mass effects in the beta-function. To this order, we also compute the Symanzik improvement coefficient necessary to remove the O(a) lattice artefacts originating from the boundaries. For reasonable lattice res olutions and the standard Wilson action, lattice artefacts are found t o be only weakly dependent on the lattice spacing a, while they vanish quickly with the improved action of Sheikholeslami and Wohlert. As a by-product we obtain the relation between the Lambda-parameters associ ated with the bare couplings of this improved and the standard Wilson action.