Finiteness of the topological models in the Landau gauge

A general procedure for showing the perturbative finiteness of topological field theories is presented. The main tools of the investigation are the existence of a supersymmetric algebra and the choice of a Landau gauge for the gauge-fixing part of the action. First the on-shell supersymmetry is introduced, then the Slavnov identity and the off-shell supersymmetric algebra, finally the quantum extensions and the perturbative finiteness are studied. As an explicit example, the three-dimensional BF-system with a nonvanishing cosmological term is discussed in details. (K.A.) 15 refs., 2 tabs