  We present the Bogoliubov's causal perturbative QFT, which includes only one
refinement: the creation-annihilation operators at a point, \emph{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.
