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

Abstract

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.