Causal perturbative QED and white noise

TL;DR

This paper integrates white noise analysis into causal perturbative QED by interpreting creation-annihilation operators as Hida operators, effectively avoiding infrared and ultraviolet divergences in the adiabatic limit.

Contribution

It introduces a novel mathematical interpretation of creation-annihilation operators using Hida operators within causal perturbative QED, simplifying divergence issues.

Findings

Avoids infrared and ultraviolet divergences in the adiabatic limit

Provides a rigorous mathematical framework for creation-annihilation operators

Maintains the structure of causal perturbative QFT

Abstract

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.