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arxiv: 2605.14122 · v1 · submitted 2026-05-13 · ✦ hep-th · hep-ph

Recognition: 1 theorem link

· Lean Theorem

Landau-Khalatnikov-Fradkin Transformations in Reduced Quantum Electrodynamics: Perturbative and Nonperturbative Dynamics of the Fermion Propagator

Anam Ashraf , Faisal Akram , M. Jamil Aslam , Dania Rodr\'iguez-Tzintzun , Adnan Bashir , Luis Albino
Authors on Pith no claims yet

Pith reviewed 2026-05-15 01:48 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords Landau-Khalatnikov-Fradkinreduced QEDfermion propagatorgauge transformationchiral condensatepole massnonperturbative
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The pith

The Landau-Khalatnikov-Fradkin transformations show that the chiral fermion condensate and pole mass are gauge-invariant in reduced quantum electrodynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper analyzes how gauge transformations affect the fermion propagator in reduced quantum electrodynamics using Landau-Khalatnikov-Fradkin transformations. It derives an all-orders analytical expression for the propagator in any covariant gauge from a reference gauge, valid both perturbatively and nonperturbatively. The authors argue that using the reference gauge ξ=1/3 simplifies calculations by making the leading logarithmic term vanish at one loop in the massless case. They expand results to two loops and examine the dynamically generated mass. Numerical computations confirm that the chiral condensate and the fermion pole mass do not depend on the gauge choice.

Core claim

Starting from the fermion propagator in a reference gauge, the Landau-Khalatnikov-Fradkin transformation provides its expression in an arbitrary covariant gauge to all orders in reduced QED. This holds for both massless and massive cases, and applies to the nonperturbative mass function. The choice of ξ = 1/3 as reference gauge eliminates the leading log in the wave-function renormalization at one loop, connecting to multiplicative renormalizability. Numerical evaluation shows the chiral condensate and pole mass are independent of gauge.

What carries the argument

The Landau-Khalatnikov-Fradkin transformation, which relates the fermion propagator in different gauges via a phase factor involving the gauge parameter difference.

Load-bearing premise

The Landau-Khalatnikov-Fradkin transformation formula from ordinary quantum electrodynamics applies directly and without modification to reduced quantum electrodynamics, including its nonperturbative version for the mass function.

What would settle it

Computing the chiral condensate via the Schwinger-Dyson equation in two different gauges independently, without using the LKF transformation, and finding a mismatch in the results.

Figures

Figures reproduced from arXiv: 2605.14122 by Adnan Bashir, Anam Ashraf, Dania Rodr\'iguez-Tzintzun, Faisal Akram, Luis Albino, M. Jamil Aslam.

Figure 1
Figure 1. Figure 1: FIG. 1. Wavefunction renormalization (top panel) and dy [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Euclidean pole mass (top panel) and chiral conden [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original 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 $\xi=1/3$, 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript derives the all-order Landau-Khalatnikov-Fradkin (LKF) transformation for the fermion propagator in reduced quantum electrodynamics (RQED), starting from a reference gauge ξ=1/3 to obtain an analytic expression valid in arbitrary covariant gauges. It expands the result perturbatively to two-loop order for massless and massive cases, compares with existing literature, motivates the reference gauge choice by the vanishing of leading logarithms, examines implications for the dynamically generated mass function, and presents numerical evidence that the chiral fermion condensate and fermion pole mass remain gauge-invariant quantities.

Significance. If the central results hold, the work supplies a practical all-order bridge between gauges in RQED, facilitating both perturbative calculations and nonperturbative studies of dynamical chiral symmetry breaking. The numerical confirmation of gauge invariance for the condensate and pole mass, together with the perturbative checks, would strengthen the reliability of Schwinger-Dyson analyses in reduced-dimensional QED models relevant to condensed-matter applications.

major comments (1)
  1. The nonperturbative application of the LKF transformation to the dressed mass function (the step underlying the numerical gauge-invariance test for the condensate and pole mass) assumes the standard 4D form carries over unmodified. In RQED the photon propagator and vertex structure differ due to reduced dimensionality; the manuscript must explicitly verify that no additional corrections arise, as this assumption is load-bearing for the claim that the transformed quantities are independently gauge-invariant rather than invariant by construction.
minor comments (2)
  1. Abstract: the statement that perturbative results are compared with the literature would be strengthened by a brief quantitative indication of agreement (e.g., coefficient matching at one- and two-loop order) or a pointer to the relevant table/figure.
  2. Numerical section: the gauge-invariance plots for the condensate and pole mass should include explicit error estimates or convergence diagnostics to allow readers to assess the robustness of the reported invariance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive overall assessment and for identifying this important point regarding the nonperturbative application of the LKF transformation. We address the comment below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: The nonperturbative application of the LKF transformation to the dressed mass function (the step underlying the numerical gauge-invariance test for the condensate and pole mass) assumes the standard 4D form carries over unmodified. In RQED the photon propagator and vertex structure differ due to reduced dimensionality; the manuscript must explicitly verify that no additional corrections arise, as this assumption is load-bearing for the claim that the transformed quantities are independently gauge-invariant rather than invariant by construction.

    Authors: We thank the referee for this observation. The LKF transformation for the fermion propagator in RQED is derived from the gauge transformation generated by the longitudinal part of the RQED photon propagator (which has the explicit form appropriate to reduced dimensionality). Because the transformation acts multiplicatively on the propagator via an exponential of an integral involving only the photon propagator, the functional form for the dressed mass function remains identical to the standard expression once the RQED photon propagator is substituted; no additional vertex-dependent corrections enter at the level of the propagator transformation itself, as the underlying Ward identity continues to hold. Nevertheless, we agree that an explicit verification should be provided. In the revised manuscript we will add a short dedicated paragraph (in the section discussing the nonperturbative application) that substitutes the RQED photon propagator into the LKF kernel, confirms the absence of extra terms, and reiterates that the numerical gauge-invariance results follow directly from this substitution rather than by construction. revision: yes

Circularity Check

0 steps flagged

Minor self-citation in LKF reference but central gauge-invariance test remains independent

full rationale

The paper starts from a reference-gauge propagator, applies the standard LKF gauge transformation to obtain all-orders expressions, and then performs numerical evaluation of the chiral condensate and pole mass after transformation. The choice of reference gauge ξ=1/3 is motivated by the explicit one-loop vanishing of the leading logarithm in the massless wave-function renormalization, which is a perturbative calculation independent of the final nonperturbative results. No equation in the provided text reduces the claimed gauge invariance to a fitted parameter or to a self-referential definition; the numerical test computes the quantities in the transformed gauge rather than enforcing invariance by construction. Self-citations to prior LKF literature exist but are not load-bearing for the RQED extension or the numerical invariance check. The derivation chain therefore contains only minor self-citation and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the standard LKF transformation to RQED without additional assumptions beyond those of covariant gauges in QED; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (1)
  • domain assumption The Landau-Khalatnikov-Fradkin transformation holds for the fermion propagator in reduced QED as in standard QED.
    Invoked to obtain the all-order expression in arbitrary gauge from the reference gauge.

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discussion (0)

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Reference graph

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