Interpretation of the solutions of the Wheeler-DeWitt equation

We extract transition amplitudes among matter constituents of the universe by applying perturbation theory to the solutions of the Wheeler-DeWitt equation. By considering the limit in which gravity is treated classically, we identify what replaces the probability amplitudes in a Schrödinger framework. This mathematical identification determines in turn the physical interpretation of the solutions of the Wheeler-DeWitt equation. The interpretation so obtained is based on the current carried by these solutions and confirms ideas put forward by A. Vilenkin.