The Wheeler–DeWitt equation is an attempt to mathematically meld the ideas of quantum mechanics and general relativity, a step toward a theory of quantum gravity. In this approach, time plays no role in the equation, leading to the problem of time. More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergmann-Komar "group" (which is the diffeomorphism group on-shell, but differs off-shell).
A Mathematical Proof That The Universe Could Have Formed Spontaneously From Nothing?