Causal perturbative QED and white noise
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 559-585
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We present Bogoliubov's causal perturbative QFT with 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 and eliminating 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 choosing the renormalization scheme). This enhances the predictive power of the theory, and in particular allows deriving nontrivial mass relations. The approach is general and can be applied to investigate any perturbative QFT.
Keywords:
scattering operator, causal perturbative method in QFT, white noise, Hida operators, integral kernel operator, Fock expansion.
@article{TMF_2024_218_3_a7,
author = {J. Wawrzycki},
title = {Causal perturbative {QED} and white noise},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {559--585},
publisher = {mathdoc},
volume = {218},
number = {3},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a7/}
}
J. Wawrzycki. Causal perturbative QED and white noise. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 559-585. http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a7/