Causal perturbative QED and white noise

TL;DR

This paper introduces a white noise analysis approach to causal perturbative QED, which avoids divergences and eliminates free parameters, thereby enhancing the theory's predictive power and enabling new mass relations.

Contribution

The paper's main contribution is interpreting creation-annihilation operators as Hida operators within causal perturbative QFT, removing divergences and free parameters.

Findings

Avoids infrared and ultraviolet divergences

Eliminates free parameters related to normalization

Derives non-trivial mass relations

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 and elimination of the free parameters of the theory, associated with the choice of normalization in computation of the retarded and advanced parts of causal distributions (corresponding to the freedom in the choice of renormalization scheme). This enhances the predictive power of the theory, and in particular allows to derive non-trivial mass relations. The approach is general and can be applied to investigate any perturbative QFT.