  The Hamiltonian approach to the quantum field theory is considered. Since
there are additional difficulties such as the Haag theorem and Stueckelberg
divergences, renormalization of the time-dependent dynamical quantum field
theory is much more complicated than renormalization of the S-matrix. It is
necessary to consider the regularized theory with ultraviolet and infrared
cutoffs and impose the conditions not only on the dependence of the Hamiltonian
on the cutoffs (as usual) but also on the dependence of the initial states. It
happens that one should consider the initial states to be singulary dependent
on the cutoffs in order to avoid the Stueckelberg divergences. Different types
of semiclassical approximations to quantum theory are discussed. It happens
that the method of quantizing classical solutions to field equations
corresponds not to the WKB-approach but to the complex-WKB theory. The problem
of imposing conditions on the semiclassical initial states is discussed.
Different prescriptions for choice of initial conditions are analysed.
