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Starting from the instant form of relativistic quantum dynamics for a systemof interacting fields, where amongst the ten generators of the Poincare grouponly the Hamiltonian and the boost operators carry interactions, we offer analgebraic method to satisfy the Poincare commutators. We do not need to employthe Lagrangian formalism for local fields with the Noether representation ofthe generators. Our approach is based on an opportunity to separate in theprimary interaction density a part which is the Lorentz scalar. It makespossible apply the recursive relations obtained in this work to construct theboosts in case of both local field models (for instance with derivativecouplings and spins $\geq1$) and their nonlocal extensions. Such models aretypical of the meson theory of nuclear forces, where one has to take intoaccount vector meson exchanges and introduce meson-nucleon vertices withcutoffs in momentum space. Considerable attention is paid to finding analyticexpressions for the generators in the clothed-particle representation, in whichthe so-called bad terms are simultaneously removed from the Hamiltonian and theboosts. Moreover, the mass renormalization terms introduced in the Hamiltonianat the very beginning turn out to be related to certain covariant integralsthat are convergent in the field models with appropriate cutoff factors.

A possible way for constructing generators of the Poincare group in quantum field theory