EFFECTIVE ACTIONS OF (2-DIMENSIONAL GRAVITY AND BF THEORY(1))

We develop the perturbation theory of the BF theory, which is equivale nt to (2+1)-dimensional gravity without a cosmological constant if we take SO(1, 2) as the gauge group. We show that the BF theory, which ma y have a Chern-Simons term, has only tree- or one-loop connected Feynm an diagrams and that the theory is completely finite (at all orders). We evaluate the effective actions of the BF theory and the generalized BF theory which has a 'cosmological constant' and show that quantum c orrections lead to 'Chern-Simons terms', using a BRST invariant regula rization based on Pauli-Villars.