Quantum effects in nonlinear insulating materials in the presence of a nonstationary electromagnetic field

A theory of quantum effects is constructed for nonlinear media whose dielectric properties depend on the time under the influence of a nonstationary pumping field. An integrodifferential equation is obtained for the vector potential of the field, and a scalar product is defined in the space of its solutions. The Hamiltonian of the radiation field is diagonalized by Bogolyubov canonical transformations, and quantities such as the number of photons produced by the medium and the degree of squeezing when squeezed states are generated are expressed in terms of the coefficients of these transformations.