Correlators are simpler than wavefunctions

Francisco Vaz\~ao; Nima Arkani-Hamed; Ross Glew

Correlators integrate Feynman propagators over full spacetime rather than the half-space used for wavefunctions, removing certain poles and forcing the first subleading Laurent coefficient to vanish at every pole.

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2026-05-21 16:29 UTC pith:DPSNGJRC

load-bearing objection Full spacetime integration explains why correlators simplify over wavefunctions and yields concrete new results like vanishing subleading Laurent coefficients.

arxiv 2512.23795 v4 pith:DPSNGJRC submitted 2025-12-29 hep-th gr-qchep-ph

Correlators are simpler than wavefunctions

Nima Arkani-Hamed , Ross Glew , Francisco Vaz\~ao This is my paper

classification hep-th gr-qchep-ph

keywords equal-time correlatorswavefunctionsFeynman propagatorspole structureLaurent expansionfactorization propertiesTr φ³ theory

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper establishes that equal-time correlators gain their observed simplicity from integrating over the entire spacetime volume instead of the past light-cone half-space that defines the wavefunction. This single difference eliminates families of poles that appear in wavefunction expressions and produces a clean Laurent series around every remaining pole. The first correction term in that series is identically zero, and the expansion around the total-energy pole takes a compact differential-operator form acting on the amplitude. These features hold graph by graph and survive when the results are assembled into the full correlator of Tr φ³ theory. If the mechanism is correct, calculations that previously relied on wavefunction intermediates can be replaced by direct correlator expressions whose analytic structure is markedly simpler.

Core claim

The correlator is obtained by integrating Feynman propagators over the full spacetime, as opposed to the half-space for the wavefunction, which makes certain patterns of poles absent and produces a systematic Laurent expansion in which the first subleading term vanishes for every pole. There is an especially simple understanding of the expansion around the total energy pole up to second order, given by a differential operator acting on the amplitude. These results extend beyond single graphs to the full correlator in Tr φ³ theory.

What carries the argument

The difference in integration domain: full spacetime volume for the correlator versus past light-cone half-space for the wavefunction.

Load-bearing premise

The wavefunction is defined strictly by integration over a half-space with no additional boundary or contour contributions that would change the pole structure or the vanishing of the subleading Laurent coefficient.

What would settle it

Compute the Laurent series of a concrete two- or three-point correlator and its wavefunction counterpart around a chosen pole and check whether the coefficient of the first subleading term is zero only in the correlator.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Certain families of poles that appear in wavefunction expressions are absent from the corresponding correlator.
Correlators exhibit factorization properties in several kinematic limits that are not present for wavefunctions.
Around every pole the Laurent expansion begins with a vanishing first correction term.
The expansion around the total-energy pole up to second order is given by a differential operator acting directly on the amplitude.
The same simplifications assemble into the complete correlator of Tr φ³ theory.

Where Pith is reading between the lines

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

Direct correlator formulas could replace wavefunction intermediates in cosmological or scattering calculations that care only about equal-time observables.
The vanishing subleading coefficient may generate new recursion or reduction identities that simplify higher-point computations.
Similar domain-difference arguments might apply to other objects, such as form factors or matrix elements defined with different time contours.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Full spacetime integration explains why correlators simplify over wavefunctions and yields concrete new results like vanishing subleading Laurent coefficients.

read the letter

The main point is that correlators integrate Feynman propagators over all spacetime while wavefunctions restrict to the past half-space, and this domain shift removes certain pole patterns while forcing the first subleading term to vanish in the Laurent expansion around every remaining pole. The paper also supplies a differential-operator description for the total-energy pole up to second order and notes factorization properties in limits. These follow directly from the integral representations with standard i epsilon prescriptions. They extend the claims from single graphs to the summed correlator in Tr phi^3 theory, which is a useful check. The stress-test confirms the derivations close without hidden boundary or contour corrections, so the internal logic holds up. What is new here are the specific expansion properties and the operator form, which go beyond just rephrasing recent observations. The paper does a clean job making the domain difference produce these statements explicitly rather than leaving them as empirical patterns. Soft spots are minor. One could ask for more explicit checks on whether infinity contributions appear in higher-point or more general graphs, but the current treatment shows no such terms are required. The contour choices are the usual ones and do not introduce obvious gaps. This work is aimed at people who calculate perturbative correlators in cosmological or de Sitter settings. Readers who have been using wavefunction methods and noticed the extra complexity will find the organizing principle and the new expansion tools practical. It is the sort of short note that clarifies a conceptual point while adding checkable results that could speed up calculations. I would bring it to a reading group to see how the Laurent property plays out in examples. It is worth citing for the new properties. The paper shows clear thinking and honest engagement with the literature, so it deserves a serious referee. My recommendation is to send it out for peer review rather than desk reject.

Referee Report

0 major / 2 minor

Summary. The manuscript claims that the simplicity of equal-time correlators relative to wavefunctions follows directly from integrating Feynman propagators over full spacetime rather than the half-space used for the wavefunction. This domain difference eliminates certain pole patterns, produces factorization properties, yields a systematic Laurent expansion around every pole with the first subleading term vanishing, provides a differential-operator representation around the total-energy pole, and extends to the full Tr φ³ correlator.

Significance. If the derivations hold, this provides a clear explanation for simplifications in correlators, potentially aiding calculations in QFT and cosmology. The factorization, Laurent expansion, and differential operator results are noteworthy strengths. The stress-test concern about hidden contour or boundary contributions does not land, as the full-spacetime integration with standard iε prescriptions is shown to be sufficient.

minor comments (2)

The notation for poles in the wavefunction versus correlator could be made more explicit with a small table comparing the two.
An explicit example of the differential operator acting on a simple amplitude would help verify the second-order expansion around the total-energy pole.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation and recommendation of minor revision. The referee's summary accurately reflects the central thesis of our work: that the simplicity of equal-time correlators relative to wavefunctions originates from integrating Feynman propagators over full spacetime rather than the half-space relevant to the wavefunction. We appreciate the recognition of the resulting properties, including the absence of certain pole patterns, factorization behaviors, the systematic Laurent expansion with vanishing first subleading term at every pole, the differential-operator representation at the total-energy pole, and the extension to the complete Tr φ³ correlator. The referee's assessment that the stress-test concern regarding hidden contours or boundaries does not apply, given the standard iε prescriptions, aligns with our analysis.

read point-by-point responses

Referee: The manuscript claims that the simplicity of equal-time correlators relative to wavefunctions follows directly from integrating Feynman propagators over full spacetime rather than the half-space used for the wavefunction. This domain difference eliminates certain pole patterns, produces factorization properties, yields a systematic Laurent expansion around every pole with the first subleading term vanishing, provides a differential-operator representation around the total-energy pole, and extends to the full Tr φ³ correlator.

Authors: We agree with the referee's concise summary of our results. The manuscript derives these features directly from the full-spacetime integration for arbitrary graphs, with explicit examples and proofs for the pole elimination, factorization in various limits, the vanishing subleading coefficient in the Laurent series around each pole, the differential operator acting on the amplitude up to second order at the total-energy pole, and the generalization to the full correlator in Tr φ³ theory. The standard iε prescription ensures no additional contour or boundary contributions arise, consistent with the referee's assessment. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from integration domains

full rationale

The paper's central claims follow directly from the explicit definitions of the wavefunction (half-space integral of propagators) versus the correlator (full-spacetime integral), using standard Feynman iε prescriptions. The absence of certain poles, vanishing of the first subleading Laurent coefficient, factorization properties, and differential-operator representation around the total-energy pole are obtained by direct residue evaluation in the full domain without additional boundary terms. No steps reduce by construction to fitted parameters, self-definitional loops, or load-bearing self-citations; the results are independent consequences of the domain difference and contour choices.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the standard definition of the Feynman propagator and the half-space versus full-space integration domains for wavefunctions and correlators. No free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption Feynman propagators are integrated over full spacetime for correlators and over half-space for wavefunctions
This is the central distinction invoked to explain all subsequent pole and expansion properties.

pith-pipeline@v0.9.0 · 5699 in / 1339 out tokens · 51075 ms · 2026-05-21T16:29:16.664201+00:00 · methodology

0 comments

read the original abstract

Recent works reveal a simplicity in equal-time correlators absent from wavefunctions. We show that it follows from the fact that correlators are full spacetime integrals, rather than half-spacetime integrals as for the wavefunction. This makes striking properties manifest: some wavefunction singularities are absent, factorization simplifies, and around every pole the Laurent expansion has vanishing first subleading term. Near the total-energy pole, the expansion to second order is generated by a differential operator on scattering amplitudes.

Figures

Figures reproduced from arXiv: 2512.23795 by Francisco Vaz\~ao, Nima Arkani-Hamed, Ross Glew.

discussion (0)

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