Санкт-Петербургский Государственный Университет Научно-Исследовательский Институт Физики Физический Факультет СПбГУ High Energy and Elementary Particles Physics
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First, we would like to recall the
long-standing 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 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".
Назад Вверх
Письмо вебмастеру
Март 2015