Causal perturbative QFT and white noise

In this paper, 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 the analysis of the causal axioms for the scattering operator with the Hida operators as the creation-annihilation operators.