Exact Results in Quantum Theory

In the talk I will present the recent results about the existence of the weak adiabatic limit in models of the perturbative quantum field theory with massless particles defined with the use of the Epstein-Glaser approach. One of the characteristic features of this approach is the use of a switching function in the intermediate steps of the construction of the scattering matrix and the interacting fields. A switching function plays the role of the infrared regularization and is removed by taking the adiabatic limit. In particular, in order to define the vacuum expectation values of the products or the time-ordered products of the interacting fields (called the Wightman and Green functions, respectively) one takes the so-called weak adiabatic limit.