Solution of the Adiabatic Limit Problem. QED Without Infinities

Abstract

In this work we give positive solution to the adiabatic limit problem in causal perturbative QED on the Minkowski space-time, as well as give a contribution to the solution of the convergence problem for the perturbative series in QED on the Minkowski space-time, by using white noise construction of free fields. The obtained scattering operator is a generalized operator sufficient for the computation of the effective cross section, involving generalized many-particle plane wave states of the fundamental fields. Bound states remain outside the scope of the resulting QED on the Minkowski space-time. The method is general enough to be applicable to more general causal perturbative QFT, such as Standard Model with the Higgs field.