Landau–Khalatnikov–Fradkin transformations in reduced quantum electrodynamics: perturbative and nonperturbative dynamics of the fermion propagator
8 affiliations
- 1Quaid-i-Azam University
- 2Air University
- 3University of the Punjab
- 4Universidad Michoacana de San Nicolás de Hidalgo
- 5Universidad de Huelva
- 6Universidad Autónoma de Querétaro
- 7División de Estudios de Posgrado e Investigación
- 8Universidad de Sonora
Abstract
We present a comprehensive analysis of the Landau–Khalatnikov–Fradkin transformations for the charged fermion propagator in reduced quantum electrodynamics (RQED). Starting from the propagator in a reference gauge, we perform a gauge transformation to obtain its analytical expression valid to all orders in an arbitrary covariant gauge and also applicable in a nonperturbative context. This work complements and extends previous studies of quantum electrodynamics in various spacetime dimensions, for both massless and massive fermions. At the perturbative level, we expand the resulting expressions up to two-loop order for both massless and massive cases, and compare our results with those available in the literature wherever possible. We argue that the most suitable choice of the reference covariant gauge in RQED is ξ =1/3 ξ = 1 / 3 , as in this case the leading logarithmic contribution to the massless wave-function renormalization vanishes at one-loop order. This choice provides a direct connection between perturbation theory and the constraints imposed by multiplicative renormalizability on the massless fermion propagator. We also investigate the implications of the Landau–Khalatnikov–Fradkin transformations for the dynamically generated mass function of the fermion propagator. Finally, through numerical computation, we demonstrate that both the chiral fermion condensate and the fermion pole mass are gauge-invariant quantities.
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BibTeX
@article{ashraf2026landaukhalatnikovfradkin,
title = {{Landau–Khalatnikov–Fradkin transformations in reduced quantum electrodynamics: perturbative and nonperturbative dynamics of the fermion propagator}},
author = {Anam Ashraf and Faisal Akram and M. Jamil Aslam and Dania Rodríguez-Tzintzun and Adnan Bashir and Luis Albino},
journal = {The European Physical Journal C},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16319-2},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16319-2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Landau–Khalatnikov–Fradkin transformations in reduced quantum electrodynamics: perturbative and nonperturbative dynamics of the fermion propagator
AU - Anam Ashraf
AU - Faisal Akram
AU - M. Jamil Aslam
AU - Dania Rodríguez-Tzintzun
AU - Adnan Bashir
AU - Luis Albino
PY - 2026
DA - 2026/10/21
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16319-2
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16319-2
AB - We present a comprehensive analysis of the Landau–Khalatnikov–Fradkin transformations for the charged fermion propagator in reduced quantum electrodynamics (RQED). Starting from the propagator in a reference gauge, we perform a gauge transformation to obtain its analytical expression valid to all orders in an arbitrary covariant gauge and also applicable in a nonperturbative context. This work complements and extends previous studies of quantum electrodynamics in various spacetime dimensions, for both massless and massive fermions. At the perturbative level, we expand the resulting expressions up to two-loop order for both massless and massive cases, and compare our results with those available in the literature wherever possible. We argue that the most suitable choice of the reference covariant gauge in RQED is ξ =1/3 ξ = 1 / 3 , as in this case the leading logarithmic contribution to the massless wave-function renormalization vanishes at one-loop order. This choice provides a direct connection between perturbation theory and the constraints imposed by multiplicative renormalizability on the massless fermion propagator. We also investigate the implications of the Landau–Khalatnikov–Fradkin transformations for the dynamically generated mass function of the fermion propagator. Finally, through numerical computation, we demonstrate that both the chiral fermion condensate and the fermion pole mass are gauge-invariant quantities.
SN - 1434-6044
SN - 1434-6052
ER -