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

We develop the perturbation theory of the BF theory, which is equivalent 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 may have a Chern-Simons term, has only tree- or one-loop connected Feynman 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 corrections lead to 'Chern-Simons terms', using a BRST invariant regularization based on Pauli-Villars.