
First, we would like to recall the longstanding problem of constructing the perturbation series for QFT with Hamiltonian containing the fields for unstable particles, that cannot be presented in the structure of Fock space. This creates a problem of unitarity. Moreover, the naive operating with Dyson's series certainly results in graphs with external legs corresponding to resonances in contradiction with conventional understanding. This problem becomes more and more actual in connection with the concept of effective theory. We consider simple renormalizable model describing the interaction of two particles: stable (with mass m) and unstable (with mass $M>2m$). We consider in detail Veltman's technique and show that there the naive Dyson series were incorrectly used. The result is as follows: the perturbation series constructed from the skeleton graphs with dressed propagators results in the Soperator which presents unitary Smatrix on the Fock space solely constructed from the stable particle states. This Smatrix fulfil the causality condition. Though the theory is nonlocal. We generalize Veltman's proof for the case when the model is less trivial and admits mixing. We also discuss methods partly described in the preprint "Diagrammar"\ by G.'t Hooft and M.Veltman and in Veltman's book "Diagrammatica".
