Asymptotic Dynamics in Quantum Field Theory - When does the coupling   switch off?
  We discuss the approach to asymptotic dynamics due to Kulish and Faddeev. We show that there are problems in applying this method to theories with four point interactions. The source of the difficulties is identified and a more general method is constructed. This is then applied to various theories including some where the coupling does switch off at large times and some where it does not. 
Robin Horan, Martin Lavelle and David McMullan