Algebra of Constraints and Solutions of Quantum Gravity

We construct the regularized Wheeler–De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for only a small subset of all wavefunctions being integrals of scalar densities this condition can be satisfied. It turns out that the resulting operator is much simpler than the one used in \cite{JK} to find exact solutions of Wheeler–De Witt equation. We proceed to finding exact solutions of quantum gravity and we discuss their interpretation making use of the quantum potential approach to quantum theory.