  Higher order renormalization in 4D quantum gravity is carried out using
dimensional regularization with great care concerning the conformal-mode
dependence. In this regularization, resummation can be automatically carried
out without making an assumption like that of David, Distler and Kawai. In this
paper we consider a model of 4D quantum gravity coupled to QED. Resummation
inevitably implies a four-derivative quantum gravity. The renormalizability is
directly checked up to $O(e_r^6)$ and $O(t_r^2)$, where $e_r$ and $t_r$ are the
running coupling constants of QED and the traceless gravitational mode. There
is no other running coupling constant in our model. The conformal mode is
treated exactly, which means it is unrenormalized. It is found that Hathrell's
results are included in our results. As a by-product, it is found that a
higher-order gravitational correction to the beta function of QED is negative.
An advantage of our model is that in the very high-energy regime, it closely
resembles exactly solvable 2D quantum gravity. Thus, we can study physical
states of 4D quantum gravity in this regime in parallel to those of 2D quantum
gravity, which can be described with diffeomorphism invariant composite fields.
