The definitions of scattering matrix and inclusive scattering matrix in the
framework of formulation of quantum field theory in terms of associative
algebras with involution are presented. The scattering matrix is expressed in
terms of Green functions on shell (LSZ formula) and the inclusive scattering
matrix is expressed in terms of generalized Green functions on shell. The
expression for inclusive scattering matrix can be used also for quasi-particles
(for elementary excitations of any translation-invariant stationary state, for
example, for elementary excitations of equilibrium state.) An interesting
novelty is the consideration of associative algebras over real numbers.
