DO METRIC INDEPENDENT CLASSICAL ACTIONS LEAD TO TOPOLOGICAL FIELD-THEORIES

We investigate the quantum theory of non-abelian BF-systems (gauge theories with the classical metric independent action integral tr BF(A)). The fact that due to a complicated (on-shell reducible) gauge structure the quantum action of these theories does not differ only by a BRST commutator from the classical action, and that moreover the BRST operator turns out to be metric dependent, renders the standard arguments for metric independence inapplicable. We establish the topological nature of these models and argue that in gauge theories the information on gauge invariance is contained entirely in the metric independent part of the BRST operator. We make some general remarks on the relation between metric independence and absence of dynamical degrees of freedom.