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arxiv: 2604.21118 · v1 · submitted 2026-04-22 · 🌀 gr-qc · hep-th

Unruh-DeWitt Detector Response in Toroidal Spacetime

Nirmalya Kajuri , Sheeshram Siddh This is my paper

Pith reviewed 2026-05-09 23:14 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Unruh-DeWitt detectortoroidal spacetimespatial topologyquantum fieldsparticle detectorscompact dimensionsMinkowski spacetime
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The pith

Local quantum detectors sense toroidal spatial topology through their response rates

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

The paper calculates how an Unruh-DeWitt detector responds to a quantum scalar field in flat four-dimensional spacetime where two spatial directions are periodically identified to form a torus. Transition rates are found for inertial motion and for uniform acceleration along either compact or non-compact directions. These rates deviate from ordinary Minkowski results because the periodic identifications alter the field's two-point correlations. The deviations depend on the compactification lengths and trajectory orientation. A sympathetic reader would care because the result supplies a concrete, local probe of global topology that curvature measurements cannot access.

Core claim

In Minkowski spacetime with spatial topology R × T² the transition rates of an Unruh-DeWitt detector are modified by the compactification scales for all three examined trajectories, because the Wightman function must include image contributions from the periodic identifications.

What carries the argument

Unruh-DeWitt monopole detector whose response is set by the Wightman function of the scalar field in periodically identified Minkowski spacetime

If this is right

  • Inertial observers register periodic modulations in excitation probability set by the torus radii.
  • Acceleration along a compact direction produces a topology-dependent modification of the effective temperature felt by the detector.
  • Acceleration along the non-compact direction still yields interference terms from the compact dimensions.
  • All topological signatures appear even though the spacetime is flat, isolating pure global-topology effects.

Where Pith is reading between the lines

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

  • The same technique could be used to map detector responses in other compact topologies such as higher-genus surfaces or different identifications.
  • In a cosmological context the method might allow local quantum measurements to place bounds on the spatial topology of the universe.
  • Quantum information protocols that rely on field correlations could be repurposed as topology sensors.

Load-bearing premise

The standard Unruh-DeWitt coupling together with the Wightman function computed in the periodically identified spacetime fully determine the detector response without further compactification or regularization effects.

What would settle it

A calculation of the inertial-detector excitation probability that shows no dependence on the compactification radii would falsify the claim that topology imprints on local detector rates.

Figures

Figures reproduced from arXiv: 2604.21118 by Nirmalya Kajuri, Sheeshram Siddh.

Figure 1
Figure 1. Figure 1: Equilibrium de-excitation rate F˙ eq(∆E) for an inertial detector on R × T 2 , computed from (21) with ∆E = −10. Top left: Rate as a function of L1 at fixed L2 = 500 for three values of the detector velocity vz. Top right: Rate as a function of L2 at fixed L1 = 500 for the same velocities. In both panels, the dashed line marks the Minkowski value −∆E/(2π). The oscillatory correction decays as the varying c… view at source ↗
Figure 2
Figure 2. Figure 2: Instantaneous excitation rate F˙ τ (∆E) as a function of the switch-on duration ∆ = τ − τ0 for the trajectory (22) with α = 1/∆E and ∆E > 0. Left: L1 = 100/∆E fixed, τ0 = 0, varying L2. Middle: L2 = 5/∆E fixed, τ0 = 0, varying L1. Right: L1 = 100/∆E, L2 = 5/∆E fixed, varying τ0. The L = ∞ curves approach the Unruh equilibrium value asymptotically, while all finite-L curves diverge at the critical duration … view at source ↗
Figure 3
Figure 3. Figure 3: Equilibrium de-excitation rate F˙ eq(∆E) for a detector accelerating along the noncompact direction, computed from (39)-(40). All quantities are expressed in units of |∆E|. Top left: Rate as a function of L1 at fixed L2 = 100/|∆E| and ∆E = −1, for four values of α. Top right: Rate as a function of L2 at fixed L1 = 100/|∆E|, same parameters. The dashed line indicates the pure Unruh value for α = 50/|∆E|. Bo… view at source ↗
read the original abstract

The global topology of spacetime, though invisible to local curvature measurements, leaves signatures on the correlation functions of quantum fields. We study these signatures using an Unruh-DeWitt particle detector operating in four-dimensional Minkowski spacetime with two spatial directions periodically identified, yielding a spatial topology $\mathbb{R}\times T^2$. We compute detector transition rates for three trajectories: uniform inertial motion, uniform proper acceleration directed along one of the compact axes, and uniform proper acceleration along the non-compact axis. Our results show how a local quantum measurement can reveal features of the large-scale spatial topology.

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

0 major / 2 minor

Summary. The manuscript studies Unruh-DeWitt detector transition rates in 4D Minkowski spacetime with two spatial directions periodically identified (R × T² topology). It computes the rates for three trajectories—inertial motion, uniform proper acceleration along a compact direction, and uniform proper acceleration along the non-compact direction—using the standard monopole coupling to the Wightman function obtained via periodic identification, and concludes that the resulting differences reveal signatures of the large-scale spatial topology.

Significance. If the calculations are correct, the work provides a clear demonstration that local quantum measurements can detect global topological features through modified field correlations, without curvature. The reliance on the conventional image-sum representation of the two-point function is a methodological strength, as it is mathematically well-defined and automatically incorporates the topology. This contributes to the literature on QFT in topologically non-trivial flat spacetimes and could inform analog gravity or cosmological models.

minor comments (2)
  1. The abstract states that transition rates were computed but does not summarize the key technical steps or any verification; expanding it slightly to mention the image-sum method and the three trajectories would improve accessibility.
  2. Section 2 (or equivalent) should explicitly state the regularization procedure for the Wightman function at coincidence points, even if it follows the standard Hadamard subtraction, to allow direct reproduction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The referee correctly identifies the core contribution: demonstrating that Unruh-DeWitt detector transition rates in R × T² spacetime encode signatures of spatial topology even in the absence of curvature. We have no specific major comments to address point by point, as none were raised.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper computes Unruh-DeWitt detector transition rates for inertial and accelerated trajectories in R x T^2 spacetime by applying the standard monopole interaction Hamiltonian to the Wightman function obtained via image-sum periodic identification of Minkowski space. This construction directly yields the topology-dependent correlations without any fitted parameters, self-referential definitions, or load-bearing self-citations that reduce the central result to its inputs. The differences between trajectories arise transparently from the modified two-point functions, and the method is the conventional, mathematically well-defined procedure for flat toroidal topologies with no reduction by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard QFT axioms and the Unruh-DeWitt model with no new free parameters or invented entities introduced in the abstract.

axioms (2)
  • standard math Quantum field theory on Minkowski spacetime with periodic spatial identifications
    The topology R x T^2 is defined by imposing periodic boundary conditions on two coordinates.
  • domain assumption Validity of the Unruh-DeWitt detector model in this background
    Assumes the two-level system with linear coupling to the scalar field responds according to the standard transition probability formula.

pith-pipeline@v0.9.0 · 5385 in / 1256 out tokens · 47019 ms · 2026-05-09T23:14:37.011357+00:00 · methodology

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