  It might seem that a choice of a time coordinate in Hamiltonian formulations
of general relativity breaks the full four-dimensional diffeomorphism
covariance of the theory. This is not the case. We construct explicitly the
complete set of gauge generators for Ashtekar's formulation of canonical
gravity. The requirement of projectability of the Legendre map from
configuration-velocity space to phase space renders the symmetry group a gauge
transformation group on configuration-velocity variables. Yet there is a sense
in which the full four-dimensional diffeomorphism group survives. Symmetry
generators serve as Hamiltonians on members of equivalence classes of solutions
of Einstein's equations and are thus intimately related to the so-called
"problem of time" in an eventual quantum theory of gravity.
