  The on shell equivalence of first order and second order formalisms for the
Einstein-Hilbert action does not hold for those actions quadratic in curvature.
It would seem that by considering the connection and the metric as independent
dynamical variables, there are no quartic propagators for any dynamical
variable. This suggests that it is possible to get both renormalizability and
unitarity along these lines. We have studied a particular instance of those
theories, namely Weyl gravity. Although the ground state of this system is
difficult to analyze, we have been able to study the physical effects of some
external sources.
