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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2507.06880 |
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| _version_ | 1866912634256752640 |
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| author | Oliveira, Orlando |
| author_facet | Oliveira, Orlando |
| contents | We investigate the Dyson-Schwinger equation for the photon-fermion one-particle irreducible vertex in QED in linear covariant gauges. The longitudinal component of this vertex is described using the Ball-Chiu basis, while its transverse part is expressed with the Kızılersu-Reenders-Pennington basis. Combining the vertex Ward-Takahashi identity with the vertex equation, we derive a set of exact, non-linear integral equations governing the transverse vertex. These equations hold for any linear covariant gauge and must be solved self-consistently. We discuss several approximations to the exact equations, generalizing results previously obtained at the perturbative one-loop level. Various kinematical configurations are also examined. Furthermore, we compute the perturbative solution of the transverse vertex Dyson-Schwinger equations for all transverse form factors and derive their perturbative asymptotic expressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: the full vertex, the transverse form factors and the perturbative solution Oliveira, Orlando High Energy Physics - Theory High Energy Physics - Phenomenology We investigate the Dyson-Schwinger equation for the photon-fermion one-particle irreducible vertex in QED in linear covariant gauges. The longitudinal component of this vertex is described using the Ball-Chiu basis, while its transverse part is expressed with the Kızılersu-Reenders-Pennington basis. Combining the vertex Ward-Takahashi identity with the vertex equation, we derive a set of exact, non-linear integral equations governing the transverse vertex. These equations hold for any linear covariant gauge and must be solved self-consistently. We discuss several approximations to the exact equations, generalizing results previously obtained at the perturbative one-loop level. Various kinematical configurations are also examined. Furthermore, we compute the perturbative solution of the transverse vertex Dyson-Schwinger equations for all transverse form factors and derive their perturbative asymptotic expressions. |
| title | The QED photon-fermion vertex from its Dyson-Schwinger equation in 4D: the full vertex, the transverse form factors and the perturbative solution |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2507.06880 |