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arxiv: 2605.18787 · v1 · pith:LHTPQZTWnew · submitted 2026-05-07 · ✦ hep-th · hep-lat

Can Euclidean lattice quantum field theory be analytically continued into Minkowski space?

B.P.Kosyakov , E.Yu.Popov , M. A. Vronsky This is my paper

Pith reviewed 2026-05-20 23:14 UTC · model grok-4.3

classification ✦ hep-th hep-lat
keywords lattice quantum field theoryWick rotationanalytic continuationEuclidean to Minkowskinonlocal form factorcontinuum limitspacetime discretization
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The pith

Euclidean lattice quantum field theory cannot be analytically continued to Minkowski space without first reaching the continuum limit.

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

The paper tests whether a quantum field theory placed on a Euclidean lattice can be returned to Minkowski spacetime through the inverse Wick rotation. It concludes that discretization turns the original local theory into one with a nonlocal form factor, making the required analytic continuation mathematically infeasible. A reader would care because lattice calculations are widely used to compute quantities ultimately interpreted in real-time Minkowski physics, implying that reliable results demand the continuum limit first.

Core claim

Discretization of spacetime converts local quantum field theory into a theory with a nonlocal form factor. For such a theory the Wick rotation is infeasible, so the analytic continuation from the Euclidean lattice to Minkowski space cannot be performed without first taking the continuum limit.

What carries the argument

The nonlocal form factor produced by lattice discretization of spacetime, which blocks the Wick rotation.

If this is right

  • Lattice data cannot be directly continued to Minkowski space; the continuum limit must precede any such continuation.
  • Nonlocality introduced by the lattice obstructs the analytic properties needed for the Wick rotation.
  • Physical quantities extracted from Euclidean lattice simulations require extrapolation to vanishing lattice spacing before Minkowski interpretation.

Where Pith is reading between the lines

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

  • This obstruction may underlie difficulties in obtaining real-time observables from lattice gauge theory simulations.
  • Alternative continuation techniques that avoid reliance on the Wick rotation could be needed for finite-lattice theories.
  • Similar nonlocality effects might appear in other discretized approaches to quantum field theory, such as finite-volume or momentum-cutoff schemes.

Load-bearing premise

The specific nonlocal form factor produced by discretization renders the Wick rotation mathematically infeasible.

What would settle it

An explicit demonstration that the inverse Wick rotation can be carried out on a discretized theory, such as a free scalar field on a finite lattice, recovering the correct Minkowski-space correlation functions without first removing the lattice spacing.

read the original abstract

In this paper, we attempt to test whether Euclidean lattice quantum field theory can be analytically continued into Minkowski space via the inverse Wick rotation. Our discussion indicates that such an analytical continuation is impossible without first taking the lattice theory to the continuum limit. The obstacle is that discretization of spacetime converts local quantum field theory into a theory with a nonlocal form factor, for which the Wick rotation is infeasible.

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 claims that Euclidean lattice quantum field theory cannot be analytically continued into Minkowski space via the inverse Wick rotation without first taking the lattice theory to the continuum limit. The central obstacle identified is that spacetime discretization converts a local quantum field theory into one possessing a nonlocal form factor, rendering the Wick rotation infeasible.

Significance. If the central claim is substantiated with explicit derivations, the result would provide a useful cautionary observation for lattice practitioners, reinforcing that direct analytic continuation from discretized theories is obstructed by the loss of locality and the associated analytic properties. The argument is consistent with standard distinctions between local continuum QFT and lattice regularizations (e.g., finite-difference operators yielding momentum-space factors such as sin(ap)/a), but currently lacks the supporting calculations needed to elevate it beyond a general statement.

major comments (1)
  1. Abstract: the central conclusion that discretization produces a nonlocal form factor rendering inverse Wick rotation infeasible is asserted without any derivation, explicit momentum-space expression for the form factor, or concrete example (such as the lattice Laplacian or Wilson fermion operator). This absence is load-bearing for the claim, as the manuscript supplies no calculation demonstrating why the specific nonlocality precludes analytic continuation while preserving causality and the correct Minkowski signature.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for providing constructive feedback. We have revised the paper to address the concerns raised regarding the lack of explicit derivations in support of our central claim.

read point-by-point responses

  1. Referee: Abstract: the central conclusion that discretization produces a nonlocal form factor rendering inverse Wick rotation infeasible is asserted without any derivation, explicit momentum-space expression for the form factor, or concrete example (such as the lattice Laplacian or Wilson fermion operator). This absence is load-bearing for the claim, as the manuscript supplies no calculation demonstrating why the specific nonlocality precludes analytic continuation while preserving causality and the correct Minkowski signature.

    Authors: We appreciate the referee's comment on the abstract. The abstract is meant to be brief, but we recognize the need for more concrete support for the claim. In the revised version of the manuscript, we have included an explicit calculation of the form factor arising from spacetime discretization. For the lattice Laplacian, the momentum-space operator becomes (2/a^2)(1 - cos(a p)) instead of p^2. We show that this replacement leads to a function that is not analytic in the complex momentum plane in the manner required for a straightforward Wick rotation back to Minkowski space. A similar analysis is provided for the Wilson fermion operator. These additions demonstrate the obstruction to analytic continuation without first taking the continuum limit, while the continuum theory recovers the local behavior and correct signature. We believe this revision makes the argument more robust and directly addresses the referee's concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central argument rests on the general observation that lattice discretization replaces local operators with nonlocal form factors (such as finite-difference momentum-space kernels) whose analytic properties preclude a direct inverse Wick rotation while preserving causality and the correct Minkowski signature. This is presented as a standard feature of cutoff theories rather than a derived result from fitted parameters, self-referential definitions, or load-bearing self-citations. No equations or steps reduce the claimed impossibility to an input by construction; the reasoning draws on established distinctions between lattice and continuum QFT without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that lattice discretization necessarily produces a nonlocal form factor blocking the Wick rotation; no free parameters or invented entities appear in the abstract.

axioms (1)
  • domain assumption Discretization of spacetime converts local quantum field theory into a theory with a nonlocal form factor
    Presented in the abstract as the key obstacle preventing the inverse Wick rotation.

pith-pipeline@v0.9.0 · 5588 in / 1203 out tokens · 54145 ms · 2026-05-20T23:14:46.048195+00:00 · methodology

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Reference graph

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