Generalized Hamiltonian formulation of a strictly localizable Lagrangian field theory

Basic axioms are formulated in terms of the properties of the coefficient functions of the generalized Bogolyubov–Shirkov HamHtonian. An advanced representation is given for these coefficient functions. The $S$ matrix is introduced into the dynamics of the theory through the generalized Bogolyubov–Shirkov Hamiltonian and the main properties of the $S$ matrix are established.