ON THE BRST CHARGE FOR TOPOLOGICAL BF THEORIES

Topological quantum field theories are discussed using the generalized canonical approach to constrained systems. We give the general structure of the canonical effective action of linearly dependent first class constrained systems. When this construction is applied to metric independent classical actions, one is able to ensure -under some explicitly given boundary conditions - metric independence of the associated partition function. The quantum analysis of the non-abelian BF theories in four dimensions is per-formed on these lines; their off-shell nilpotent BRST charge is constructed and a new direct proof of the topological nature of the associated quantum theories is presented. We do also comment on some properties of the BF actions in higher dimensions.