Asymptotic dynamics in quantum field theory

A crucial element of scattering theory and the LSZ reduction formula is the assumption that the coupling vanishes at large times. This is known not to hold for the theories of the Standard Model and in general such asymptotic dynamics is not well understood. We give a description of asymptotic dynam ics in field theories which incorporates the important features of weak con vergence and physical boundary conditions. Applications to theories with th ree and four point interactions are presented and the results are shown to be completely consistent with the results of perturbation theory. (C) 2000 American Institute of Physics. [S0022-2488(00)02907-8].