  The space-time features of the relativistic dynamics are analyzed in the
framework of the time dependent propagator theory. The adiabatic hypothesis is
substituted by the disturbative adiabatic hypothesis, resulting with the
corresponding space-time regionalization of scattering processes. The other
kind of generalization introduces forms of the propagator theory for the
particle systems whose propagation is based on the family of spacelike
surfaces. The mathematical basis is established allowing the definition of the
corresponding, generalized propagators and amplitudes.
