  Quantum gravity is analyzed from the viewpoint of the renormalization group.
The analysis is based on methods introduced by J. Polchinski concerning the
perturbative renormalization with flow equations. In the first part of this
work, the program of renormalization with flow equations is reviewed and then
extended to effective field theories that have a finite UV cutoff. This is done
for a scalar field theory by imposing additional renormalization conditions for
some of the nonrenormalizable couplings. It turns out that one so obtains a
statement on the predictivity of the effective theory at scales far below the
UV cutoff. In particular, nonrenormalizable theories can be treated without
problems in the proposed framework. In the second part, the standard covariant
BRS quantization program for Euclidean Einstein gravity is applied. A momentum
cutoff regularization is imposed and the resulting violation of the
Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization
group equation for Euclidean quantum gravity, the predictivity of effective
quantum gravity at scales far below the Planck scale is investigated with flow
equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor
identities is proposed and it is argued that in the effective quantum gravity
context, the restoration will only be accomplished with finite accuracy.
Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the
viewpoint of the Polchinski method. It is speculated whether a limit with
nonvanishing gravitational constant might exist where the latter would
ultimatively be determined by the cosmological constant and the masses of the
elementary particles.
