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arxiv: 2605.18945 · v1 · pith:X2PKPNKQnew · submitted 2026-05-18 · 🪐 quant-ph · gr-qc· hep-th

Non-perturbative measurements of two-point functions in quantum field theory

Sebastian Holm\'en , T. Rick Perche This is my paper

Pith reviewed 2026-05-20 11:08 UTC · model grok-4.3

classification 🪐 quant-ph gr-qchep-th
keywords two-point functionquantum field theoryparticle detectorsnon-perturbative methodsdetector correlationsoperational stateslattice probesspacetime multipole
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The pith

A lattice of gapless detectors extracts the two-point function of a quantum field from their measurable correlations.

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

The paper develops a non-perturbative protocol that lets local probes access the two-point function of a quantum field inside a spacetime region. A lattice of gapless particle detectors is arranged so that chosen probe observables encode the field's smeared two-point function through their correlations. A spacetime multipole expansion quantifies the discrepancies that arise from the finite size of the interaction regions. The result is an expression for the two-point function written entirely in terms of detector correlations, which supplies an operational definition of states in quantum field theory.

Core claim

The central claim is that the two-point function of the quantum field can be recovered non-perturbatively by measuring correlations among a lattice of gapless detectors whose probe observables are selected to map directly onto the smeared field correlator.

What carries the argument

A lattice of gapless particle detectors whose probe observables are chosen to encode the field's two-point function.

Load-bearing premise

The selected probe observables on the lattice encode the smeared two-point function without uncontrolled back-reaction or higher-order detector-field interactions that would break the mapping.

What would settle it

Measure the correlations of the detector lattice in a controlled free scalar field and check whether they reproduce the known two-point function once the multipole corrections for finite interaction regions are subtracted.

Figures

Figures reproduced from arXiv: 2605.18945 by Sebastian Holm\'en, T. Rick Perche.

Figure 1
Figure 1. Figure 1: The pointlike (blue), smeared (orange), and leading [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The two-point function for the Minkowski vacuum [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: The two-point function for the Minkowski vacuum [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: The classical solution ϕ0(x) associated with the coherent state |g0⟩ with δ = 3/2ℓ in the (t, x) plane. The black dot denotes the event xi used in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The difference between the correlation function of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The two point function for the one particle [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We present a non-perturbative method through which local probes can access the two-point function of a quantum field within a region of spacetime. By considering a lattice of gapless particle detectors, we identified the probe observables that encode the field's two-point function. We quantify the discrepancies introduced by physical finite-sized interaction regions by performing a spacetime multipole expansion of the smeared two-point function. Our protocol expresses the two-point function entirely in terms of measurable detectors correlations, providing an operational notion of states in QFT.

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 / 2 minor

Summary. The manuscript presents a non-perturbative protocol to extract the two-point function of a quantum field from correlations measured by a lattice of gapless particle detectors. Probe observables are identified that encode the smeared field two-point function, with a spacetime multipole expansion used to quantify finite-size discrepancies in the interaction regions. The central claim is that the two-point function can be expressed entirely in terms of measurable detector correlations, yielding an operational notion of states in QFT.

Significance. If the central mapping holds, the work would be significant for operational approaches to QFT and quantum information. It attempts to move beyond perturbative detector models by providing a direct, non-perturbative link between measurable correlations and field correlators, which could be relevant for defining states in curved spacetime or strongly coupled regimes. The multipole expansion offers a controlled treatment of smearing effects, and the emphasis on measurable quantities is a positive feature.

major comments (1)
  1. [Abstract and protocol derivation] Abstract and protocol section: the claim that the two-point function is expressed 'entirely in terms of measurable detector correlations' and is non-perturbative assumes negligible back-reaction and higher-order interaction terms. The spacetime multipole expansion addresses only finite-size smearing discrepancies and does not control dynamical back-reaction or non-linear detector-field effects that can arise at finite coupling for gapless detectors with continuous spectra. This assumption is load-bearing for the exact mapping and requires explicit justification or bounds.
minor comments (2)
  1. [Abstract] The abstract refers to 'gapless particle detectors' without specifying the interaction Hamiltonian or the precise form of the probe observables; these should be stated explicitly early in the manuscript for clarity.
  2. [Introduction] Additional references to prior work on Unruh-DeWitt detectors and operational reconstructions of QFT states would help situate the contribution.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying this important point about the assumptions underlying our protocol. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract and protocol derivation] Abstract and protocol section: the claim that the two-point function is expressed 'entirely in terms of measurable detector correlations' and is non-perturbative assumes negligible back-reaction and higher-order interaction terms. The spacetime multipole expansion addresses only finite-size smearing discrepancies and does not control dynamical back-reaction or non-linear detector-field effects that can arise at finite coupling for gapless detectors with continuous spectra. This assumption is load-bearing for the exact mapping and requires explicit justification or bounds.

    Authors: We thank the referee for highlighting this subtlety. Our derivation establishes an exact algebraic mapping between the chosen detector observables and the smeared field two-point function within the linear interaction Hamiltonian; no perturbative expansion in the coupling is performed either in the field evolution or in the inversion step that recovers the correlator. The qualifier 'non-perturbative' therefore refers to the absence of perturbative QFT techniques rather than to an arbitrary coupling strength. We do, however, work in the regime where the detector-field coupling is weak enough that back-reaction on the field state remains negligible, which is the standard assumption in the Unruh-DeWitt literature that allows detectors to function as probes. The spacetime multipole expansion controls only the finite-size smearing error, as the referee correctly notes. To make the domain of validity explicit, we will revise the abstract and the protocol section to state the weak-coupling assumption and add a short paragraph (with references to existing analyses of back-reaction for gapless detectors) that discusses when the approximation holds. This clarification will be incorporated in the next version. revision: yes

Circularity Check

0 steps flagged

Protocol expresses two-point function via detector correlations without reduction to inputs

full rationale

The paper derives a non-perturbative protocol by considering a lattice of gapless detectors and identifying probe observables that encode the smeared two-point function, then applying a spacetime multipole expansion to quantify finite-size discrepancies. No equations reduce the claimed mapping to a fitted parameter renamed as prediction, nor does any load-bearing step rely on self-citation chains or ansatzes imported from prior author work. The central claim remains independent of its inputs, as the operational extraction follows from the detector-field interaction model and multipole corrections rather than tautological redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on standard QFT detector models and the validity of the multipole expansion for finite regions; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Gapless particle detectors interact with the quantum field in a manner that allows their correlations to encode the field's two-point function.
    This is the core modeling choice that lets the protocol work.

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    exp 2i ˜Gi + i∆ij + iEij −exp −2i ˜Gi −i∆ ij −iE ij −exp 2i ˜Gi −i∆ ij −iE ij + exp −2i ˜Gi + i∆ij + iEij # 21 = X µ1,µ′ 1=± ... µN ,µ′ N=± i 2N e−2Hii

    Computing D ˆσ(i) y ˆσ(j) x E and D ˆσ(j) y ˆσ(i) x E The matrix representation will in this case be ˆσ(i) y ˆσ(j) x =   0 0 i 0 0 0 0−i −i 0 0 0 0 i 0 0   ,(B26) giving us the table of eigenvalues µ′ i µ′ j µi µj µ′ iµ′ j ˆσ(i) y ˆσ(j) x |µiµj⟩ + + - + i + - - - −i - + + + −i - - + - i . By inserting these, term by term, into Eq. (B9) we obtain all...

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  71. [71]

    Writing the local expected value in this form, we can use the methods developed in the previous subsections

    Computing⟨ˆσ (i) z ⟩ Let us start by noticing that⟨ˆσ (i) z ⟩=⟨ˆσ (i) z I(j)⟩. Writing the local expected value in this form, we can use the methods developed in the previous subsections. We obtain the matrix ˆσ(i) z I(j) =   0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0   ,(B33) giving us the non-zero matrix components 22 µ′ i µ′ j µi µj µ′ iµ′ j ˆσ(i) z I(j) |µ...

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  72. [72]

    Non-zero expected values The remaining expected values of up to two Pauli matrices not listed in the previous are all zero, apart from the identity on every detector, which is of course 1. For convenience the nonzero expected values we have calculated are listed below: ⟨ˆσ(i) z ˆσ(j) z ⟩= 1 2 e−(Hii+Hjj)  e2Hij NY k=1 k̸=i,j cos(2Gik −2G jk) +e −2Hij N...

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  73. [73]

    Multipole moments in general spacetimes Let us start by defining the multipoles of the spacetime smearing functions integrated in Riemann normal coordinates without, incorporating the leading order expansion of the volume element of Eq. (E9). We call these quantities the flatmultipoles of Λ xi. For instance, the flat monopole, dipole, and quadrupole are g...

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  74. [74]

    (E7) to compute the leading order terms of multipole expansion of the smeared Wightman function

    Leading order multipole expansion of the Wightman function Let us now use Eq. (E7) to compute the leading order terms of multipole expansion of the smeared Wightman function. The leading order multipole expansion is W(Λ xi ,Λ xj) =W(x i,x j)ΛxiΛxj (E16) +W α(xi,x j)Λα xiΛxj +W µ′(xi,x j)ΛxiΛµ′ xj + 1 2 Wαβ(xi,x j)Λαβ xi Λxj + 1 2 Wµ′ν′(xi,x j)ΛxiΛµ′ν′ xj ...

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  75. [75]

    (E17) vanish since the Ricci tensor vanish in Minkowski spacetime

    Minkowski Spacetime To estimate the error in Minkowski spacetime we will use the fact that the kernel to the Wightman distribution may be written as W(x,x ′) = 1 4π2 −(t−t ′)2 + (¯x−¯x′)2 ,(E18) We also note that the first two terms of orderℓ 2 in Eq. (E17) vanish since the Ricci tensor vanish in Minkowski spacetime. To obtain the final two terms we need ...

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