Toth, Gabor Zsolt2009-04-222011-09-072009-04-222011-09-072009-04-22https://openscience.sissa.it/handle/1963/3621A comparison of the methods of averaging and adiabatic switching for the definition of the infinite time limit of the time evolution operator in scattering theory is presented. The focus is on certain basic features which are relevant mainly in quantum field theory. Specifically, the differences between the unitarity properties of the operators obtained using the two methods, the difference between the necessary energy renormalizations and the existence of Lippmann-Schwinger equations are discussed. The manifestation of these differences in perturbation expansions is also described.140978 bytesapplication/pdfen-USPreprint