St-Petersburg State University Research Institute of Physics Faculty of Physics High Energy and Elementary Particles Physics
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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 S-operator which presents unitary
S-matrix on the Fock space solely constructed from the stable particle
states. This S-matrix fulfil the causality condition. Though the
theory is non-local. 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".
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March 2009