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Causal perturbative QED and white noise

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Abstract

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.

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Notes

  1. One important motivation is the clear separation of the UV and infrared (IR) divergence problems: the UV infinities occur in the splitting of causal distributions into retarded and advanced parts, and the IR infinities are located in the adiabatic limit \(g_0\to\text{const}\) problem. Another benefit is a significant simplification of the analysis of the renormalizability and unitarity of the theory with non-Abelian gauges [4], [5], [8].

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Acknowledgments

The author expresses his deep gratitude to Professor D. Kazakov and Professor I. Volovich for the very helpful discussions. He is also grateful for the excellent work conditions at JINR, Dubna. He thanks Professor M. Jeżabek for the excellent conditions for work at INP PAS in Kraków, Poland, and Professor A. Staruszkiewicz and Professor M. Jeżabek for the warm encouragement. The author acknowledges the referees for their suggestions.

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia

    J. Wawrzycki

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Correspondence to J. Wawrzycki.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, 2024, Vol. 218, pp. 559–585 https://doi.org/10.4213/tmf10298.

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Wawrzycki, J. Causal perturbative QED and white noise. Theor Math Phys 218, 483–502 (2024). https://doi.org/10.1134/S0040577924030085

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