Average effective potential for the conformal factor

We discuss a method of quantization which produces a nontrivial effective potential for the conformal factor of the metric, both in the case of matter fields propagating in a fixed background geometry, and in the case of pure gravity. In particular, using the method of the average effective potential, we compute the scale dependence of the conformal factor. We offer some speculations on the possible significance of our results. © 1995.