Canonical quantization of gravity and quantum field theory in curved space-time

It is shown that canonical quantization of gravity and matter leads to quantum field theory in curved space-time in the gravitational field can be regarded as a classical background field. The Tomonaga-Schwinger equation for matter in a background field is derived. The physical meaning of momentum constraints of quantum gravity in the presence of matter is established. As an example, the Bianchi type I cosmology is studied and the direction of alteration of evolution caused by created particles is found. (author)