On the Elimination of the Stueckelberg Divergences in the Hamiltonian Field Theory

The Stueckelberg divergences arise in the Hamiltonian approach to quantum field theory. To eliminate these divergences, certain conditions are imposed not only on the dependence of the counterterms on the regularization parameters but also on the dependence of the initial state vector on these parameters. A class of evolution-invariant initial conditions is constructed. This class can be constructed both by the Faddeev-type transformation and by the Bogolyubov method based on the consideration of the theory with smooth switching on the interaction. These methods are illustrated by a simple example of the Stueckelberg divergences that arise when calculating the particle-decay rate and are applied to the analysis of the Hamiltonian semiclassical field theory. A condition on the initial data for the Schrödinger equation is obtained in the leading order of the complex-germ theory.