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].