  A version of the quantum theory of gravity based on the concept of the wave
functional of the universe is proposed. To determine the physical wave
functional, the quantum principle of least action is formulated as a secular
equation for the corresponding action operator. Its solution, the wave
functional, is an invariant of general covariant transformations of space-time.
In the new formulation, the history of the evolution of the universe is
described in terms of coordinate time together with arbitrary lapse and shift
functions, which makes this description close to the formulation of the
principle of general covariance in the classical theory of Einstein's gravity.
In the new formulation of the quantum theory, an invariant parameter of the
evolutionary time of the universe is defined, which is a generalization of the
classical geodesic time, measured by a standard clock along time-like
geodesics.
