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arxiv: 1907.10942 · v1 · pith:E2FHUHMFnew · submitted 2019-07-25 · ✦ hep-th

Quantum Instabilities of Solitons

H. Weigel This is my paper

Pith reviewed 2026-05-24 16:20 UTC · model grok-4.3

classification ✦ hep-th
keywords solitonvacuum polarizationquantum instabilitydegenerate vacuaone-plus-one dimensionsfield theoryenergy correction
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0 comments X

The pith

Vacuum polarization energies destabilize solitons that connect degenerate vacua with different curvatures in field space.

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

The paper computes the vacuum polarization energies for several soliton solutions in one-plus-one-dimensional scalar field theories. These solitons are field configurations that interpolate between distinct but energetically degenerate vacua. Explicit results for a sample of such models lead the author to conjecture that the polarization contribution produces an instability precisely when the two vacua differ in their curvature measured in field space.

Core claim

From the considered sample solitons we conjecture that the vacuum polarization contribution to the total energy leads to instabilities whenever degenerate vacua with different curvatures in field space are accessible to the soliton.

What carries the argument

Vacuum polarization energy of soliton maps between degenerate vacua whose second derivatives of the potential differ.

If this is right

  • Solitons become unstable when they can reach vacua whose curvatures in field space are unequal.
  • The one-loop correction to the soliton energy is negative in such cases.
  • Models whose vacua share the same curvature remain stable against this mechanism.

Where Pith is reading between the lines

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

  • If the conjecture is general, classically stable solitons in a broader class of models would be eliminated once quantum corrections are included.
  • The result suggests a diagnostic: compare the second derivatives of the potential at the two vacua before deciding whether a soliton solution can survive quantization.

Load-bearing premise

The limited sample of soliton models examined is representative enough to support a general conjecture linking vacuum curvature differences to instabilities via polarization energy.

What would settle it

A computation of the vacuum polarization energy for at least one additional soliton model in which the connected vacua have equal curvature yet the total energy is still lowered, or in which the curvatures differ yet no instability appears.

Figures

Figures reproduced from arXiv: 1907.10942 by H. Weigel.

Figure 1
Figure 1. Figure 1: figure 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIGURE 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIGURE 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIGURE 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
read the original abstract

We compute the vacuum polarization energies for a couple of soliton models in one space and one time dimensions. These solitons are mappings that connect different degenerate vacua. From the considered sample solitons we conjecture that the vacuum polarization contribution to the total energy leads to instabilities whenever degenerate vacua with different curvatures in field space are accessible to the soliton.

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 / 0 minor

Summary. The manuscript computes the vacuum polarization energies for a couple of soliton models in 1+1 dimensions. These solitons are mappings connecting different degenerate vacua. From the sample computations the authors conjecture that the vacuum polarization contribution to the total energy produces instabilities whenever degenerate vacua with different curvatures in field space are accessible to the soliton.

Significance. If the conjecture holds beyond the examined cases it would identify a mechanism linking vacuum curvature mismatch to soliton instabilities via polarization energy. The computations on the sample models constitute the sole support; no general derivation or symmetry argument is supplied.

major comments (1)
  1. Abstract: the central claim is presented as a conjecture drawn from computations on only two models. No argument is given showing why curvature mismatch must produce instability in any model where such vacua are accessible, making the generality of the conjecture load-bearing and unsupported by the provided evidence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the report. We address the major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [—] Abstract: the central claim is presented as a conjecture drawn from computations on only two models. No argument is given showing why curvature mismatch must produce instability in any model where such vacua are accessible, making the generality of the conjecture load-bearing and unsupported by the provided evidence.

    Authors: We agree that the conjecture is drawn from computations on the two models examined and that the manuscript contains no general derivation or symmetry argument establishing the result for arbitrary models. The abstract already qualifies the statement as a conjecture suggested by the sample solitons. To make the limited scope clearer, we will revise the abstract to state explicitly that the conjecture is motivated by the specific models considered, without implying it has been shown to hold in all cases where such vacua are accessible. revision: yes

Circularity Check

0 steps flagged

No circularity: conjecture explicitly empirical from explicit model computations

full rationale

The paper computes vacuum polarization energies for a small number of explicit 1+1D soliton models that connect degenerate vacua, then states a conjecture based on the observed pattern in that sample. No derivation chain, fitted parameter, or self-citation is invoked to claim the result follows by construction or uniqueness theorem. The central statement is labeled a conjecture whose generality rests on the representativeness of the examined cases, not on any reduction of the claimed link to the input data or prior self-citations. This is a standard non-circular empirical observation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities can be extracted from the provided text.

pith-pipeline@v0.9.0 · 5558 in / 968 out tokens · 22484 ms · 2026-05-24T16:20:55.617364+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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matches
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supports
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extends
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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Krakow Lectures on Scalar Quantum Solitons

    hep-th 2026-05 unverdicted novelty 7.0

    The paper presents Linearized Soliton Perturbation Theory (LSPT) as a new Hamiltonian tool for constructing quantum soliton states and computing their perturbative corrections and scattering.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [1]

    Rajaraman, Solitons and Instantons (North Holland, Amsterdam, New Y ork, 1982)

    R. Rajaraman, Solitons and Instantons (North Holland, Amsterdam, New Y ork, 1982)

    work page 1982

  2. [2]

    Graham, M

    N. Graham, M. Quandt, and H. Weigel, Lect. Notes Phys. 777, p. 1 (2009)

    work page 2009

  3. [3]

    J. S. Faulkner, J. Phys. C10, p. 4661 (1977)

    work page 1977

  4. [4]

    Weigel, Phys

    H. Weigel, Phys. Lett. B766, p. 65 (2017)

    work page 2017

  5. [5]

    Weigel, M

    H. Weigel, M. Quandt, and N. Graham, Phys. Rev. D97, p. 036017 (2018)

    work page 2018

  6. [6]

    Alonso-Izquierdo and J

    A. Alonso-Izquierdo and J. M. Guilarte, Nucl. Phys. B852, p. 696 (2011)

    work page 2011

  7. [7]

    Alonso-Izquierdo and J

    A. Alonso-Izquierdo and J. M. Guilarte, JHEP 01, p. 125 (2014)

    work page 2014

  8. [8]

    M. A. Lohe, Phys. Rev. D20, p. 3120 (1979)

    work page 1979

  9. [9]

    M. A. Lohe and D. M. O’Brien, Phys. Rev. D23, p. 1771 (1981)

    work page 1981

  10. [10]

    Weigel, Adv

    H. Weigel, Adv. High Energy Phys. 2017, p. 1486912 (2017)

    work page 2017

  11. [11]

    Roma´ nczukiewicz, Phys

    T. Roma´ nczukiewicz, Phys. Lett. B773, p. 295 (2017)

    work page 2017

  12. [12]

    Bazeia, M

    D. Bazeia, M. J. dos Santos, and R. F. Ribeiro, Phys. Lett . A208, p. 84 (1995)

    work page 1995

  13. [13]

    Alonso-Izquierdo and J

    A. Alonso-Izquierdo and J. Mateos Guilarte, Annals Phy s. 327, p. 2251 (2012)

    work page 2012

  14. [14]

    M. A. Shifman and M. B. V oloshin, Phys. Rev. D57, p. 2590 (1998)

    work page 1998

  15. [15]

    Weigel and N

    H. Weigel and N. Graham, Phys. Lett. B783, p. 434 (2018)

    work page 2018