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

J. Wawrzycki

Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 394-443

Résumé

We present Bogoliubov's causal perturbative QFT with a single 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 the existence proof for 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,”, which eliminates the arbitrariness in choosing the splitting that makes the theory definite, with its predictive power considerably strengthened. We present the example of a charge–mass relation that can be proved within this theory and is confirmed experimentally.

Détail

Keywords: scattering operator, causal perturbative method in QFT, interacting fields, white noise, Hida operators, integral kernel operators, Fock expansion.