  In a former paper we proposed a model for the quantization of gravity by
working in a bundle $E$ where we realized the Hamilton constraint as the
Wheeler-DeWitt equation. However, the corresponding operator only acts in the
fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt
equation and express the Hamilton constraint differently, either with the help
of the Hamilton equations or by employing a geometric evolution equation. There
are two modifications possible which both are equivalent to the Hamilton
constraint and which lead to two new models. In the first model we obtain a
hyperbolic operator that acts in the fibers as well as in the base space and we
can construct a symplectic vector space and a Weyl system.
  \nd In the second model the resulting equation is a wave equation in $\so
\times (0,\infty)$ valid in points $(x,t,\xi)$ in $E$ and we look for solutions
for each fixed $\xi$. This set of equations contains as a special case the
equation of a quantized cosmological Friedmann universe without matter but with
a cosmological constant, when we look for solutions which only depend on $t$.
Moreover, in case $\so$ is compact we prove a spectral resolution of the
equation.
