  Starting from the space of Lorentzian metrics, we examine the full
gravitational path integral in 3 and 4 space-time dimensions. Inspired by
recent results obtained in a regularized, dynamically triangulated formulation
of Lorentzian gravity, we gauge-fix to proper-time coordinates and perform a
non-perturbative ``Wick rotation'' on the physical configuration space. Under
certain assumptions about the behaviour of the partition function under
renormalization, we find that the divergence due to the conformal modes of the
metric is cancelled non-perturbatively by a Faddeev-Popov determinant
contributing to the effective measure. We illustrate some of our claims by a 3d
perturbative calculation.
