  Starting from the instant form of relativistic quantum dynamics for a system
of interacting fields, where amongst the ten generators of the Poincare group
only the Hamiltonian and the boost operators carry interactions, we offer an
algebraic method to satisfy the Poincare commutators. We do not need to employ
the Lagrangian formalism for local fields with the Noether representation of
the generators. Our approach is based on an opportunity to separate in the
primary interaction density a part which is the Lorentz scalar. It makes
possible apply the recursive relations obtained in this work to construct the
boosts in case of both local field models (for instance with derivative
couplings and spins $\geq1$) and their nonlocal extensions. Such models are
typical of the meson theory of nuclear forces, where one has to take into
account vector meson exchanges and introduce meson-nucleon vertices with
cutoffs in momentum space. Considerable attention is paid to finding analytic
expressions for the generators in the clothed-particle representation, in which
the so-called bad terms are simultaneously removed from the Hamiltonian and the
boosts. Moreover, the mass renormalization terms introduced in the Hamiltonian
at the very beginning turn out to be related to certain covariant integrals
that are convergent in the field models with appropriate cutoff factors.
