  Problems connected with non-Hamiltonian nature of low energy nucleon dynamics
in the effective field theory (EFT) of nuclear forces is investigated by using
the formalism of the generalized quantum dynamics (GQD) developed in [J. Phys.
A, 5657 (1999)]. This formalism is based on a generalized dynamical equation
derived as the most general equation of motion consistent with the current
concepts of quantum physics. By using the example of the EFT of nuclear forces,
we demonstrate that a theory, which, being formulated in terms of Hamiltonian
formalism, leads to ultraviolet divergences, may manifest itself as a perfectly
consistent theory free from infinities, if it is considered from the more
general point of view provided by the GQD. We show that non-Hamiltonian
character of nucleon dynamics gives rise to some new problems connected with
discontinuity of the evolution operator. This discontinuity results in the fact
that the Hilbert space of nucleon states cannot be realized in the standard
way. A space which allows one to realize, in a natural way, the Hilbert space
of nucleon states is investigated. The structure of this space reflects the
existence of the high energy degrees of freedom which affect on low energy
nucleon dynamics.
