Geodesic
On the~Landau--Khalatnikov--Fradkin transformation in quenched $\mathrm{QED}_3$
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 548-558

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We present the results of studies of the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in $d=3-2\varepsilon$. Assuming the finiteness of the perturbative expansion, i.e., the existence of the limit $\varepsilon\to 0$, we show that exactly for $d=3$ all odd perturbative coefficients starting from the third order must be equal to zero in any gauge. To test this, we calculate three- and four-loop corrections to the massless fermion propagator. Three-loop corrections are finite and gauge invariant, while four-loop corrections have singularities. The terms depending on the gauge parameter are completely determined by the lower orders in accordance with the Landau–Khalatnikov–Fradkin transformation.
Keywords: quantum electrodynamics, gauge dependence
Mots-clés : fermion propagator, multiloop calculations. 
@article{TMF_2023_216_3_a12,
     author = {A. V. Kotikov},
     title = {On {the~Landau--Khalatnikov--Fradkin} transformation in quenched $\mathrm{QED}_3$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {548--558},
     publisher = {mathdoc},
     volume = {216},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a12/}
}
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A. V. Kotikov. On the~Landau--Khalatnikov--Fradkin transformation in quenched $\mathrm{QED}_3$. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 548-558. http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a12/