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arxiv: 2604.16035 · v1 · submitted 2026-04-17 · ✦ hep-th

Coulomb Potential in Podolsky-Carroll-Field-Jackiw Electrodynamics

D. S. Cabral , L. A. S. Evangelista , A. F. Santos This is my paper

Pith reviewed 2026-05-10 07:32 UTC · model grok-4.3

classification ✦ hep-th
keywords Podolsky electrodynamicsCarroll-Field-Jackiw termLorentz violationCoulomb potentialMøller scatteringphoton propagatornonrelativistic limit
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0 comments X

The pith

A Lorentz-violating term reintroduces short-distance divergences into Podolsky electrodynamics.

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

Podolsky electrodynamics adds a higher-derivative term to Maxwell theory that changes the photon dispersion and removes short-distance divergences. The paper combines this with the Carroll-Field-Jackiw model, which introduces a fixed background four-vector that breaks Lorentz symmetry. The photon propagator is derived for the joint theory and inserted into Møller scattering to extract the interaction between charges. The result is that the background vector restores the ultraviolet divergence that Podolsky had eliminated. In the nonrelativistic regime the potential receives separate contributions from the spatial part of the vector, which picks out a preferred direction, and from its timelike part, which alters the dispersion.

Core claim

In the combined Podolsky-Carroll-Field-Jackiw framework the photon propagator produces a Coulomb potential in which the Carroll-Field-Jackiw contribution reintroduces the short-distance divergence suppressed by the Podolsky term; both the spatial component that breaks isotropy and the timelike component that affects dispersion enter the nonrelativistic interaction potential.

What carries the argument

The photon propagator obtained from the Podolsky-CFJ Lagrangian, used to compute the Møller scattering amplitude that yields the interaction potential.

If this is right

  • The force between static charges diverges again at very small separations.
  • Electromagnetic interactions acquire a preferred spatial direction set by the background vector.
  • The energy relation for interacting particles is modified by the timelike component.
  • The potential ceases to be the standard Coulomb form and acquires direction-dependent corrections.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Combining higher-derivative regularization with Lorentz violation may cancel the benefits of each in the ultraviolet regime.
  • Precision tests of the Coulomb law at short range could place bounds on the size of the combined corrections.
  • The induced anisotropy might appear in atomic energy levels or scattering cross-sections if the background vector is nonzero.

Load-bearing premise

The derivation assumes a perturbative expansion around the combined Lagrangian together with the validity of the nonrelativistic limit without higher-order corrections or gauge choices that could alter the divergence structure.

What would settle it

An explicit evaluation of the short-distance potential that remains finite, or a direct measurement showing the force between charges stays isotropic and divergence-free when a nonzero Carroll-Field-Jackiw vector is present.

Figures

Figures reproduced from arXiv: 2604.16035 by A. F. Santos, D. S. Cabral, L. A. S. Evangelista.

Figure 1
Figure 1. Figure 1: Feynman diagrams for Møller scattering. The first diagram corresponds to the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Coulomb potential for different values of the parameters [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original abstract

Podolsky electrodynamics, a higher-derivative extension of Maxwell's theory characterized by the Podolsky parameter $\lambda=1/m$, which modifies the photon dispersion relation and regularizes short-distance divergences, is investigated. This framework is then coupled to the Carroll-Field-Jackiw (CFJ) model, in which a Lorentz-violating background four-vector is introduced. Within this extended electrodynamics, the photon propagator is obtained in the combined Podolsky-CFJ framework and subsequently applied to M\"{o}ller scattering. It is shown that the CFJ contribution can reintroduce the short-distance divergence suppressed by Podolsky's term. In the nonrelativistic limit, both the spatial component--which introduces a preferred direction in space and thus breaks isotropy--and the timelike component--which directly affects the dispersion relation--contribute nontrivially to the interaction potential.

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

0 major / 2 minor

Summary. The paper studies Podolsky electrodynamics (higher-derivative regularization via parameter λ=1/m) coupled to the Carroll-Field-Jackiw (CFJ) Lorentz-violating term with a background four-vector. It derives the photon propagator in the combined theory, applies it to Møller scattering, shows that the CFJ term reintroduces short-distance divergences suppressed by the Podolsky factor, and extracts the nonrelativistic Coulomb potential, finding nontrivial contributions from both timelike (affecting dispersion) and spacelike (breaking isotropy) components of the CFJ vector.

Significance. If the derivations hold, the result illustrates the tension between higher-derivative UV regularization and Lorentz-violating corrections in a controlled perturbative setting. The explicit nonrelativistic potential, obtained directly from the modified propagator without fitted parameters, provides a concrete, falsifiable expression that could be tested in systems sensitive to preferred directions or modified dispersion relations. The work is grounded in the model Lagrangian and standard Fourier-transform techniques for the static potential.

minor comments (2)
  1. The nonrelativistic reduction and the extraction of the potential at q^0=0 would benefit from an explicit statement of the gauge choice and the order in velocity at which higher corrections are neglected, to confirm that the divergence reappearance is not an artifact of the approximation.
  2. Notation for the CFJ four-vector components (timelike vs. spacelike) and the Podolsky parameter should be introduced once and used consistently; the current presentation leaves the precise decomposition in the potential formula somewhat implicit.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful summary of the manuscript, the positive assessment of its significance, and the recommendation for minor revision. We accept the recommendation and will prepare a revised version incorporating any necessary clarifications or corrections. No specific major comments were listed in the report, so we have no point-by-point rebuttals to provide.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper derives the photon propagator from the combined Podolsky-CFJ Lagrangian, applies it to Møller scattering, and extracts the nonrelativistic potential via Fourier transform at q^0=0. The claimed reintroduction of short-distance divergence and the nontrivial contributions from timelike/spacelike CFJ components follow directly from the high-momentum expansion of that propagator (Podolsky ~1/k^4 plus linear CFJ correction) without any fitted parameters renamed as predictions, without load-bearing self-citations, and without ansatz smuggling or uniqueness theorems imported from prior work. The derivation remains self-contained within the model equations and standard perturbative techniques.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard construction of the Podolsky Lagrangian, the CFJ term, and the usual rules for obtaining propagators and potentials in quantum field theory.

free parameters (2)
  • Podolsky parameter λ = 1/m
    Introduced by hand to modify the photon dispersion and suppress short-distance divergences.
  • CFJ background four-vector
    External Lorentz-violating vector whose components are treated as fixed inputs.
axioms (2)
  • standard math Standard perturbative quantum field theory rules for deriving the photon propagator from the quadratic action.
    Invoked to obtain the propagator in the combined theory.
  • domain assumption Validity of the nonrelativistic limit for extracting the Coulomb potential from the scattering amplitude.
    Used to isolate the interaction potential between charges.

pith-pipeline@v0.9.0 · 5464 in / 1331 out tokens · 47942 ms · 2026-05-10T07:32:43.765238+00:00 · methodology

discussion (0)

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Reference graph

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