  The quantum theory can be formulated in the language of positive functionals
on Weyl or Clifford algebra ($L$-functionals). It is shown that this language
gives simple understanding of diagrams of Keldysh formalism (that coincide in
our case with the diagrams of thermo-field dynamics). The matrix elements of
the scattering matrix in the formalism of $L$-functionals are related to
inclusive cross-sections, therefore we suggest the name "inclusive scattering
matrix" for this notion. The inclusive scattering matrix can be expressed in
terms of on-shell values of generalized Green functions. This notion is
necessary if we want to analyze collisions of quasiparticles.
