PARTIAL SUMMATION OF THE NONLOCAL EXPANSION FOR THE GRAVITATIONAL EFFECTIVE ACTION IN 4 DIMENSIONS

The vacuum action for the gravitational field admits a known expansion in powers of the Ricci tensor with nonlocal operator coefficients (fo rm factors). We show that going over to a different basis of curvature invariants makes a partial summation of this expansion possible. Only the fc rm factors of the Weyl-tensor invariants need to be calculated . The full action is then uniquely recovered to all orders front the k nowledge of the trace anomaly. We present an explicit expression for t he partially summed action, and point out simplifications resulting in the vertex functions. An application to the effect of the vacuum grav itational waves is discussed.