Quantum field theory with the non-Fock asymptotic fields: existence of the S matrix

The family of relativistically invariant generating functionals for the non-Fock representations of canonical commutation relations is built up. The first order by the coupling constant of the corresponding quantum field theory, having the ψ(x) free field as an in-asymptotics, complying with such a functional, is analyzed. The unitarity equivalence of the free asymptotic out- and in-fields in the first order is proved and thereby the existence of the unitary scattering matrix is proved. It is proved simultaneously that in contrast to the standard case the S matrix does not coincide with the general chronologically ordered exponent from the Lagrangian of interaction