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Using the Maslov--Shvedov method of complex germ, we show that quantum fieldtheory S-matrix can exist outside perturbation theory in the principal order ofquasiclassical approximation only under the condition that the tangentsymplectic transformation to the evolution operator of non-linear classicalfield equation is unitarily implementable in the Fock space. However, theresults of Maslov--Shvedov's book imply that this condition is seemingly alwayssatisfied.

A necessary condition for existence of S-matrix outside perturbation theory