Theory of thin shells in general relativity: Equivalence of direct and Wheeler-DeWitt quantizations

We justify the way of the direct quantization which means immediate quantization of a conservation law. It is shown that this approach is equivalent to introducing the super Hamiltonian on a minisuperspace in spirit of the Wheeler-DeWitt's approach. Then we will have: (i) all values are observable and have an obvious physical meaning and well-defined application domain; (ii) wave function is well-defined without time slicing and often can be exactly obtained; (iii) we can take off major mathematical troubles, and therefore, more complicate models can be considered exactly without the perturbation theory.