  It is shown that when the Einstein-Hilbert Lagrangian is considered without
any non-covariant modifications or change of variables, its Hamiltonian
formulation leads to results consistent with principles of General Relativity.
The first-class constraints of such a Hamiltonian formulation, with the metric
tensor taken as a canonical variable, allow one to derive the generator of
gauge transformations, which directly leads to diffeomorphism invariance. The
given Hamiltonian formulation preserves general covariance of the
transformations derivable from it. This characteristic should be used as the
crucial consistency requirement that must be met by any Hamiltonian formulation
of General Relativity.

General Relativity and Quantum Cosmology;High Energy Physics - Theory