Renormalization and O(α)-improvement of the static axial current

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schroedinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its relation to other schemes is computed to 1-loop order and the 2-loop anomalous dimension is derived. In finite volume renormalization schemes such as the SF-scheme, the renormalization scale dependence of the renormalized quantities is described by the step scaling function which can be computed by MC-simulations. We evaluate its lattice spacing effects in perturbation theory. (orig.)