  We reexamine the relationship between the path integral and canonical
formulation of quantum general relativity. In particular, we present a formal
derivation of the Wheeler-DeWitt equation from the path integral for quantum
general relativity by way of boundary variations. One feature of this approach
is that it does not require an explicit 3+1 splitting of spacetime in the bulk.
For spacetimes with a spatial boundary, we show that the dependence of the
transition amplitudes on spatial boundary conditions is determined by a
Wheeler-DeWitt equation for the spatial boundary surface. We find that
variations in the induced metric at the spatial boundary can be used to
describe time evolution---time evolution in quantum general relativity is
therefore governed by boundary conditions on the gravitational field at the
spatial boundary. We then briefly describe a formalism for computing the
dependence of transition amplitudes on spatial boundary conditions. Finally, we
argue that for nonsmooth boundaries, meaningful transition amplitudes must
depend on boundary conditions at the joint surfaces.
