BRST approach to minimal models

We introduce a BRST charge in a series of Coulomb gas models in two dimensions. We show that these models, once restricted to BRST states, are equivalent to the minimal two-dimensional conformal invariant models of Belavin, Polyakov and Zamolodchikov. Primary chiral fields are identified with BRST invariant vertex operators with screening charges. These operators are non-vanishing if and only if the 'fusion rules' are fulfilled. As an application, we prove a Feigin-Fuks integral representation for general n-point functions on the plane and on the torus. (orig.)