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arxiv: 2604.05082 · v1 · submitted 2026-04-06 · ✦ hep-th

Recognition: 1 theorem link

· Lean Theorem

Worldline Images for Yang-Mills Theory within Boundaries

Santiago Christiansen Murguizur , Lucas Manzo , Pablo Pisani
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:03 UTC · model grok-4.3

classification ✦ hep-th
keywords worldline formalismmethod of imagesYang-Mills theoryboundarieseffective actionSeeley-DeWitt coefficientsgluon productionheat kernel
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The pith

A worldline method of images computes the one-loop effective action for Yang-Mills theories on manifolds with boundaries.

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

The paper develops a worldline technique that adapts the method of images to Yang-Mills fields and their ghosts on spaces with boundaries. It treats both relative and absolute boundary conditions uniformly and incorporates the full non-Abelian structure. The construction is checked by reproducing the first three Seeley-DeWitt coefficients of the heat kernel. The same technique is then used to evaluate the rate at which gluons are produced by a constant chromoelectric background in the presence of a boundary.

Core claim

The method of images extends to the worldline representation of Yang-Mills theory, allowing the one-loop effective action to be expressed as a sum over closed paths that include image charges satisfying the chosen boundary conditions for both vector and ghost fields.

What carries the argument

Worldline path integral with image charges for relative or absolute boundary conditions applied to gauge and ghost fields.

If this is right

  • The one-loop effective action on a bounded manifold is obtained by integrating worldline paths that bounce off the boundary via image charges.
  • The first three Seeley-DeWitt coefficients are recovered for both relative and absolute boundary conditions.
  • The rate of gluon pair production in a uniform chromoelectric field is modified by the presence of a boundary.
  • Both vector and ghost contributions are included on the same footing.

Where Pith is reading between the lines

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

  • The same image technique could be applied to compute Casimir energies or vacuum energies for non-Abelian fields between parallel plates.
  • Extension to time-dependent backgrounds would allow study of particle creation in expanding universes with boundaries.
  • The method may simplify calculations of Wilson-loop expectation values near boundaries.

Load-bearing premise

The image construction reproduces the correct boundary conditions for non-Abelian gauge fields and ghosts without extra corrections.

What would settle it

A mismatch between the gluon production rate computed with this worldline-image method and an independent calculation using standard heat-kernel or Feynman-diagram techniques would falsify the construction.

Figures

Figures reproduced from arXiv: 2604.05082 by Lucas Manzo, Pablo Pisani, Santiago Christiansen Murguizur.

Figure 1
Figure 1. Figure 1: Visual representation of the different metrics defined [PITH_FULL_IMAGE:figures/full_fig_p022_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Instantons with n = 1 corresponding to a direct (blue) contribution and with n = 5 corresponding to an indirect (red) contribution. The positive integer n corresponds to the index n in (5.9) that refers to the singularities in the heat trace. point with its image across the boundary. Note that the use of worldline instantons allows one to explore non-quadratic actions. 6 Conclusions In this work we develop… view at source ↗
read the original abstract

In this article we develop a worldline technique based on the method of images to study the effective action associated to Yang-Mills theories on manifolds with boundaries. We consider the possibility of having either relative or absolute boundary conditions, which are particular types of mixed boundary conditions. Both vector fields and ghost fields are taken into account in this analysis. As a check of our construction, we compute the first three Seeley-DeWitt coefficients of the heat kernel asymptotics. Finally, we employ our technique to calculate the rate of gluon production due to a chromoelectric field background in the presence of a boundary.

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 / 3 minor

Summary. The paper develops a worldline technique based on the method of images to study the effective action for Yang-Mills theories on manifolds with boundaries. It considers relative or absolute boundary conditions for vector and ghost fields, verifies the approach by computing the first three Seeley-DeWitt coefficients of the heat kernel, and applies the method to calculate the gluon production rate due to a chromoelectric field in the presence of a boundary.

Significance. If the construction holds, it provides an efficient method for incorporating boundary effects into worldline calculations for non-Abelian gauge theories, which is significant for applications in quantum field theory with boundaries, such as in condensed matter or particle physics contexts. The computation of the Seeley-DeWitt coefficients offers a direct and standard test of the method's consistency, and the gluon production calculation demonstrates its practical utility. This builds on standard techniques without introducing fitted parameters.

major comments (1)
  1. [§4 (Seeley-DeWitt coefficients)] The manuscript reports computing the first three coefficients as a consistency check, but to confirm the extension to non-Abelian fields and ghosts under the specified boundary conditions, explicit expressions or numerical values and their comparison to literature results should be provided; mismatches would indicate issues in the image method application.
minor comments (3)
  1. [Abstract] The abstract is clear but could briefly state the main result of the gluon production rate calculation for completeness.
  2. [Introduction] Additional references to previous applications of the method of images in worldline formalisms for scalar or Abelian fields would help contextualize the novelty.
  3. [Notation] The distinction between relative and absolute boundary conditions could be illustrated with a simple example early in the text for clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [§4 (Seeley-DeWitt coefficients)] The manuscript reports computing the first three coefficients as a consistency check, but to confirm the extension to non-Abelian fields and ghosts under the specified boundary conditions, explicit expressions or numerical values and their comparison to literature results should be provided; mismatches would indicate issues in the image method application.

    Authors: We agree that displaying the explicit expressions and numerical values for the first three Seeley-DeWitt coefficients, together with direct comparisons to the corresponding literature results, will make the consistency check more transparent and will better confirm the correct implementation of the image method for non-Abelian vector and ghost fields under relative and absolute boundary conditions. In the revised manuscript we will add these results in Section 4, including the separate contributions from the vector and ghost sectors and a brief discussion of their agreement with known heat-kernel coefficients for Yang-Mills theory with boundaries. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper introduces a worldline image technique for Yang-Mills fields (including ghosts) under relative/absolute boundary conditions, verifies the construction by direct computation of the first three Seeley-DeWitt coefficients of the heat kernel (an independent external benchmark), and applies the method to gluon production in a chromoelectric background. No load-bearing step reduces by definition, by fitted-parameter renaming, or by self-citation chain to its own inputs; the Seeley-DeWitt check would falsify the image construction if inconsistent, confirming the derivation remains self-contained against standard heat-kernel asymptotics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on extending established worldline and image methods to Yang-Mills with boundaries; no new free parameters, invented entities, or ad-hoc axioms beyond standard QFT assumptions are indicated.

axioms (1)
  • domain assumption The method of images applies to the worldline representation of Yang-Mills vector and ghost fields under relative or absolute boundary conditions.
    This extension is the core of the new construction and is invoked throughout the technique development.

pith-pipeline@v0.9.0 · 5392 in / 1227 out tokens · 58106 ms · 2026-05-10T19:03:45.375660+00:00 · methodology

discussion (0)

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extends
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Reference graph

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