Bogoliubov's causal perturbative QED and white noise. Interacting fields

Abstract: We present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically interpreted as the Hida operators from the 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 present here existence proof of the adiabatic limit for interacting fields in causal QED with Hida operators. This limit exists if and only if the normalization in the Epstein-Glaser splitting of the causal distributions, in the construction of the scattering operator, is "natural", and thus eliminates arbitrariness in the choice of the splitting making the theory definite, with its predictive power considerably strengthened. For example, we present a charge-mass relation which can be proved within this theory, and which is confirmed experimentally.