Strong-field QED in the Furry-picture momentum-space formulation: Ward identities and Feynman diagrams

U. Hernandez Acosta (Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany; Center for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf, Untermarkt 20, 02826 Görlitz, Germany) ; B. Kämpfer (Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany; Institut für Theoretische Physik, TU Dresden, 01062 Dresden, Germany)

The impact of a strong electromagnetic background field on otherwise perturbative QED processes is studied in the momentum-space formulation. The univariate background field is assumed to have finite support in time, thus being suitable to provide a model for a strong laser pulse in plane-wave approximation. The usually employed Furry picture in position space must be equipped with some regularizing procedure, also to ensure the Ward identity. The momentum space formulation allows generically for an easy and systematic account of such expressions, both globally and order-by-order in the weak-field expansion. In the limit of an infinitely long-acting (monochromatic) background field, these terms become gradually suppressed, and the standard perturbative QED Feynman diagrams are recovered in the leading-order weak-field limit. A few examples of three- and four-point amplitudes are considered to demonstrate the application of our Feynman rules which employ free Dirac spinors, the free photon propagator, and the free fermion propagator, while the external field impact is solely encoded in the fermion-fermion-photon vertex function. Properties of the latter vertex function are elaborated in some detail. The appearance of on/off shell contributions, singular structures, and Oleinik resonances is pointed out.

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      "value": "The impact of a strong electromagnetic background field on otherwise perturbative QED processes is studied in the momentum-space formulation. The univariate background field is assumed to have finite support in time, thus being suitable to provide a model for a strong laser pulse in plane-wave approximation. The usually employed Furry picture in position space must be equipped with some regularizing procedure, also to ensure the Ward identity. The momentum space formulation allows generically for an easy and systematic account of such expressions, both globally and order-by-order in the weak-field expansion. In the limit of an infinitely long-acting (monochromatic) background field, these terms become gradually suppressed, and the standard perturbative QED Feynman diagrams are recovered in the leading-order weak-field limit. A few examples of three- and four-point amplitudes are considered to demonstrate the application of our Feynman rules which employ free Dirac spinors, the free photon propagator, and the free fermion propagator, while the external field impact is solely encoded in the fermion-fermion-photon vertex function. Properties of the latter vertex function are elaborated in some detail. The appearance of on/off shell contributions, singular structures, and Oleinik resonances is pointed out."
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Published on:
20 July 2023
Publisher:
APS
Published in:
Physical Review D , Volume 108 (2023)
Issue 1
DOI:
https://doi.org/10.1103/PhysRevD.108.016013
arXiv:
2303.12941
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: