Causal perturbative QED and white noise

We will briefly present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point (for a specific momentum) are mathematically interpreted as the Hida operators from white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared (and ultraviolet) divergences in the transition to the adiabatic limit for interacting fields. We will present the essence of the argument for the removal of IR divergence in passing to the adiabatic limit $g \to 1$ for interacting fields and for the removal of UV divergence. In order to illustrate the Epstein-Glaser method for the removal of UV divergence we consider a particular one loop contribution to the scattering operator. We give a rigorous formulation, as a theorem, of a particular result concerning the adiabatic limit $g \to 1$ for interacting fields.