  Using the Maslov--Shvedov method of complex germ, we show that quantum field
theory S-matrix can exist outside perturbation theory in the principal order of
quasiclassical approximation only under the condition that the tangent
symplectic transformation to the evolution operator of non-linear classical
field equation is unitarily implementable in the Fock space. However, the
results of Maslov--Shvedov's book imply that this condition is seemingly always
satisfied.
