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arxiv: 2606.23389 · v1 · pith:HQDKYYFHnew · submitted 2026-06-22 · 🌀 gr-qc · hep-ph

Scattered wave functions and worldline instantons for particle production in curved spacetime

Philip Semr\'en , Greger Torgrimsson This is my paper

Pith reviewed 2026-06-26 07:47 UTC · model grok-4.3

classification 🌀 gr-qc hep-ph
keywords pair productioncurved spacetimescattered wave functionsworldline instantonsspin-1/2 particlesgravitational backgroundsnonperturbative methodstwo-dimensional metrics
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The pith

Two extended methods compute particle-antiparticle pair production in curved spacetimes depending on multiple coordinates.

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

The paper develops two complementary techniques for calculating the production of spin-1/2 particle pairs in gravitational backgrounds that vary nontrivially in more than one coordinate. It extends the scattered-wave-function method from electromagnetic to curved spacetime cases and derives the pre-exponential factor for the open-worldline-instanton approach. Tests on several two-dimensional metrics show that the two methods produce matching probabilities. The scattered-wave-function method gives numerically exact results efficiently in these examples, while the instanton method scales better to higher dimensions and extreme regimes.

Core claim

We extend the scattered-wave-function method to curved spacetime backgrounds and complete the open-worldline-instanton method by deriving its pre-exponential factor. When both are applied to several two-dimensional metrics the resulting pair-production probabilities agree well.

What carries the argument

The scattered-wave-function method adapted to curved spacetime and the open-worldline-instanton method with its newly derived pre-exponential factor.

If this is right

  • The two methods agree on the pair-production probabilities for the two-dimensional metrics considered.
  • The scattered-wave-function approach supplies numerically exact results and is efficient for the tested cases.
  • The instanton approach offers favorable scaling to higher-dimensional backgrounds and more extreme parameter regimes.
  • These methods supply new tools for studying pair production in multidimensional gravitational backgrounds.

Where Pith is reading between the lines

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

  • The agreement between methods in two dimensions indicates they could be applied to three-dimensional metrics where other approaches fail.
  • Worldline instantons might link to similar semiclassical techniques used in other nonperturbative quantum processes.
  • The efficiency of the scattered-wave-function method could allow systematic scans over families of curved metrics.

Load-bearing premise

The extensions of both the scattered-wave-function and worldline-instanton techniques remain valid for metrics that depend nontrivially on more than one coordinate.

What would settle it

A specific two-dimensional metric in which the two methods produce clearly different probabilities would show that at least one extension is invalid.

Figures

Figures reproduced from arXiv: 2606.23389 by Greger Torgrimsson, Philip Semr\'en.

Figure 1
Figure 1. Figure 1: FIG. 1. Spectrum of pair production with [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The line [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Same as Fig. 1 but with [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The line [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The function in (87) with [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The spectrum for the metrics in Fig. 5. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Similar to Fig. 1 but for the field in (87) with [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

We study the production of spin-$1/2$ particle-antiparticle pairs in curved spacetimes with nontrivial dependence on more than one coordinate. To this end, we develop two complementary approaches. First, we extend the scattered-wave-function (SWF) method, originally introduced for pair production in electromagnetic backgrounds, to curved spacetime backgrounds. Second, we complete the development of an open-worldline-instanton method by deriving the pre-exponential factor of the pair-production probability. We apply both methods to several two-dimensional metrics and find good agreement between the resulting probabilities. While the SWF approach provides numerically exact results and is particularly efficient for the examples considered here, the instanton approach offers favorable scaling to higher-dimensional backgrounds and more extreme parameter regimes. These methods provide new tools for studying pair production in multidimensional gravitational backgrounds beyond the reach of many existing approaches.

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 paper extends the scattered-wave-function (SWF) method, originally for electromagnetic backgrounds, to curved spacetimes and completes the open-worldline-instanton method by deriving the pre-exponential factor for the pair-production probability. Both are applied to several two-dimensional metrics with nontrivial dependence on both coordinates, yielding numerically agreeing probabilities for spin-1/2 pair production; the SWF method is noted as numerically exact and efficient for these cases while the instanton method scales better to higher dimensions.

Significance. If the extensions are valid, the work supplies complementary calculational tools for pair production in multidimensional gravitational backgrounds that lie beyond the reach of many standard approaches in QFT in curved spacetime, with the instanton route offering favorable scaling.

major comments (1)
  1. [Abstract] Abstract and introduction: the central claim that the extensions remain valid for metrics with nontrivial dependence on more than one coordinate is supported only by numerical agreement between the two newly extended methods; because both derive from the same underlying mode-decomposition and semiclassical framework, this agreement does not exclude the possibility of shared systematic error in the multi-coordinate handling, and no independent benchmark (exactly solvable case or third method) is reported.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introduction: the central claim that the extensions remain valid for metrics with nontrivial dependence on more than one coordinate is supported only by numerical agreement between the two newly extended methods; because both derive from the same underlying mode-decomposition and semiclassical framework, this agreement does not exclude the possibility of shared systematic error in the multi-coordinate handling, and no independent benchmark (exactly solvable case or third method) is reported.

    Authors: We respectfully disagree that the methods share a systematic error from a common framework. The SWF method is a direct numerical solution of the Dirac equation via scattering (numerically exact, as noted in the report) and was extended from its original electromagnetic formulation; it involves no semiclassical approximation. The open-worldline-instanton method is a distinct semiclassical approach whose pre-exponential factor is newly derived here. Agreement between an exact method and a semiclassical one on 2D metrics with nontrivial dependence on both coordinates therefore validates the multi-coordinate extensions. While an exactly solvable case or third method would be desirable, none is available for these general metrics, and the SWF results serve as the independent benchmark for the instanton results. No revision is required. revision: no

Circularity Check

0 steps flagged

No circularity: two independent method extensions cross-validated on shared test metrics

full rationale

The paper derives an extension of the scattered-wave-function method and a completion of the worldline-instanton method (pre-exponential factor) from the standard QFT-in-curved-space framework, then applies both to the same 2D example metrics and reports numerical agreement. Neither derivation reduces to the other by construction, no parameter is fitted from one method to predict the other, and no load-bearing uniqueness theorem or ansatz is imported solely via self-citation. The agreement functions as an external consistency check between distinct calculational routes rather than a self-referential identity. The central claim therefore retains independent content and is self-contained against the benchmarks the authors themselves compute.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central results rest on the validity of the analytic continuations and saddle-point approximations implicit in both methods when applied to non-static, multidimensional metrics. No explicit free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The scattered-wave-function and worldline-instanton formalisms can be extended to curved backgrounds with nontrivial dependence on more than one coordinate while preserving their essential structure.
    This is the premise that allows the two methods to be applied beyond the one-dimensional cases treated in prior work.

pith-pipeline@v0.9.1-grok · 5677 in / 1268 out tokens · 15423 ms · 2026-06-26T07:47:34.170338+00:00 · methodology

discussion (0)

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Reference graph

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