  We calculate the effective action in Yang-Mills and scalar \phi^4 quantum
field theory with quantized scale invariant metric treated non-perturbatively
in d=4 dimensions. There is no charge renormalization in the one-loop order for
matter fields. We show that the electromagnetic energy of point charges can be
finite. The temperature dependence of the effective action in inflationary
models is changed substantially as a result of an interaction with quantum
gravity.
