Canonical quantization of gravity and a problem of scattering

Linearized theory of gravity is quantized both in a naive way and as a proper limit of the Dirac-Wheeler-De Witt approach to the quantization of the full theory. The equivalence between the two approaches is established. The problem of scattering in the canonically quantized theory of gravitation is investigated. The concept of the background metric naturally appears in the canonical formalism for this case. The equivalence between canonical and path-integral approaches is established for the problem of scattering. Some kinematical properties of functionals in Wheeler superspace are studied in an appendix.