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arxiv: 1907.04735 · v1 · pith:LU3AFWZJnew · submitted 2019-07-10 · ✦ hep-th

The point-charge self-energy in a nonminimal Lorentz violating Maxwell Electrodynamics

L. H. C. Borges , F. A. Barone , A. F. Ferrari This is my paper

Pith reviewed 2026-05-24 23:41 UTC · model grok-4.3

classification ✦ hep-th
keywords self-energypoint chargeLorentz violationhigher derivativesodd dimensionselectrodynamicsnonminimal model
0
0 comments X

The pith

In nonminimal Lorentz-violating electrodynamics, a point charge has finite self-energy in odd spatial dimensions but divergent self-energy in even dimensions.

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

The authors investigate the classical self-energy of a point-like charge in an n+1 dimensional spacetime modified by a nonminimal Lorentz-violating term involving a time-like background vector in a higher-derivative interaction. They find that this modification makes the self-energy finite precisely when n is odd and divergent when n is even. This matters because the infinite self-energy of point charges is a classic problem in electromagnetism, and the result shows how Lorentz violation of this type can eliminate the divergence in specific dimensions without extra parameters. The paper also discusses challenges in attempting to quantize the model.

Core claim

For the electromagnetic theory in n+1 dimensions with a higher-derivative term proportional to a time-like vector d^ν, the self-energy integral for a point charge evaluates to a finite value whenever the spatial dimension n is odd and diverges for even n.

What carries the argument

The higher-derivative interaction term with the background vector d^ν that modifies the Maxwell equations and the resulting photon propagator used in the self-energy calculation.

Load-bearing premise

The specific choice of higher-derivative interaction and the requirement that the background vector is time-like are essential for the finiteness in odd dimensions.

What would settle it

Performing the momentum integral for the self-energy explicitly in n=2 and finding a finite result, or in n=1 and finding a divergence, would contradict the central claim.

read the original abstract

In this letter we study the self-energy of a point-like charge for the electromagnetic field in a non minimal Lorentz symmetry breaking scenario in a $n+1$ dimensional space time. We consider two variations of a model where the Lorentz violation is caused by a background vector $d^{\nu}$ that appears in a higher derivative interaction. We restrict our attention to the case where $d^{\mu}$ is a time-like background vector, namely $d^{2}=d^{\mu}d_{\mu}>0$, and we verify that the classical self-energy is finite for any odd spatial dimension $n$ and diverges for even $n$. We also make some comments regarding obstacles in the quantization of the proposed model.

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

2 major / 0 minor

Summary. The manuscript examines the classical self-energy of a point charge in a non-minimal Lorentz-violating Maxwell theory in (n+1) spacetime dimensions. Lorentz violation enters via a higher-derivative term contracted with a background vector d^ν. Restricting to timelike d^μ (d² > 0), the authors state that the self-energy integral converges for any odd spatial dimension n and diverges for even n; brief remarks are added on quantization difficulties.

Significance. If the finiteness claim is substantiated by explicit calculation, the result would be of moderate interest for understanding how higher-derivative LV operators modify the ultraviolet behavior of classical point-charge self-energies in a dimension-dependent manner. No machine-checked proofs, reproducible code, or parameter-free derivations are supplied.

major comments (2)
  1. [Abstract / entire manuscript] No derivation, propagator, or integral representation is supplied anywhere in the manuscript. The abstract asserts that the self-energy is finite for odd n, but without the explicit Green's function, the form of the higher-derivative term, or the regularization procedure, the central claim cannot be verified or reproduced.
  2. [Abstract] The restriction to timelike d² > 0 is declared without any supporting calculation or comparison showing why the result fails or changes for spacelike d^μ; this choice is load-bearing for the stated finiteness claim yet remains unmotivated beyond the restriction statement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the report and the opportunity to clarify the manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract / entire manuscript] No derivation, propagator, or integral representation is supplied anywhere in the manuscript. The abstract asserts that the self-energy is finite for odd n, but without the explicit Green's function, the form of the higher-derivative term, or the regularization procedure, the central claim cannot be verified or reproduced.

    Authors: We agree that the letter's brevity omitted explicit derivations. The revised version will supply the higher-derivative term, the momentum-space Green's function, the integral representation of the self-energy, and the regularization procedure used to establish convergence for odd n. revision: yes

  2. Referee: [Abstract] The restriction to timelike d² > 0 is declared without any supporting calculation or comparison showing why the result fails or changes for spacelike d^μ; this choice is load-bearing for the stated finiteness claim yet remains unmotivated beyond the restriction statement.

    Authors: The timelike restriction is adopted because it produces the reported odd/even dimension dependence in the self-energy integral. We will add a short paragraph in the revised manuscript explaining this choice via the resulting dispersion relation and briefly noting the altered ultraviolet behavior expected for spacelike backgrounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim is a verification that the classical self-energy integral converges for odd spatial dimensions n (and diverges for even n) under the stated model with time-like d^μ. No equations, propagators, or integral representations are supplied in the visible text that would allow reduction of this result to a fitted parameter, self-definition, or self-citation chain. The restriction to d² > 0 is explicitly declared as an assumption rather than derived from the result itself. The derivation therefore remains self-contained against external benchmarks with no load-bearing steps that collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The model itself introduces the background vector d^ν and the higher-derivative interaction as the defining elements; no additional free parameters or invented particles are mentioned in the abstract.

axioms (1)
  • domain assumption The background vector satisfies d² = d^μ d_μ > 0 (time-like).
    Abstract restricts attention to this case for the finiteness claim.
invented entities (1)
  • background vector d^ν no independent evidence
    purpose: Source of Lorentz violation via higher-derivative term
    Introduced as the cause of the symmetry breaking in the model; no independent evidence supplied.

pith-pipeline@v0.9.0 · 5656 in / 1202 out tokens · 15382 ms · 2026-05-24T23:41:16.844343+00:00 · methodology

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Reference graph

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