  We present evidence that there is a 4D model that satisfies the conditions of
renormalizability and diffeomorphism invariance simultaneously at the 2-loop
level. The traceless mode is treated perturbatively, while the conformal mode
can be managed exactly. The two conditions constrain the theory strongly and
determine the measure of the gravitational field uniquely. Quantum corrections
of the cosmological constant are computed in part to 3-loop diagrams. The
method to remove the negative-metric states is also discussed from the
viewpoint of diffeomorphism invariance in analogy to the $R_{\xi}$ gauge in
spontaneously broken gauge theory. The model may be a candidate for a continuum
version of 4D simplicial quantum geometry realized in recent numerical
simulations.

High Energy Physics - Theory