Space-Time Noncommutative Field Theories And Unitarity

Jaume Gomis; Thomas Mehen (Caltech)

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Space-Time Noncommutative Field Theories And Unitarity

Jaume Gomis, Thomas Mehen (Caltech)

High Energy Physics - Theory · Submitted 14 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Field theories with space-time noncommutativity do not have a unitary S-matrix.

how it is stated · asserted 1.00 read the record →

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,765 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.32 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriate description of string theory. Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the perturbative unitarity of noncommutative scalar field theories.	contribution 1.00	0.91	0.05	unclear 0.70
s1	Field theories with space-time noncommutativity do not have a unitary S-matrix.	result 1.00	0.62	0.76	asserted 1.00
s2	Field theories with only space noncommutativity are perturbatively unitary.	result 1.00	0.64	0.21	asserted 1.00
s3	This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field.	interpretation 0.99	0.14	0.05	asserted 0.89
s4	On the other hand, there is no regime in which space-time noncommutative field theory is an appropriate description of string theory.	interpretation 0.62	0.52	0.15	asserted 1.00
s5	Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected.	interpretation 0.64	0.49	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.63.

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arXiv listing abstract v2

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full text
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references and citing sentences
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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriate description of string theory. Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected.

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References

Forward citations

Cited by 20 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Holography with Null Boundaries
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D1-D5-F1 string theory in a non-commutative decoupling limit yields a holographic correspondence for spacetimes with a null boundary, interpolating between AdS3 and a six-dimensional asymptotic metric.
IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
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In noncommutative Yukawa theory, the CPT-required pair of interaction orderings converts the one-loop ultraviolet quadratic divergence into an infrared pole that is reachable in the s-channel.
IIA/B, Wound and Wrapped
hep-th 2000-09 accept novelty 7.0 of 10

The NCOS limit of IIA/B string theory exists without D-branes and produces a Wound String Theory that unifies all p+1 NCOS, OM, and ODp theories as states of a single framework.

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Non-Relativistic Closed String Theory
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Constraining non-commutative geometry with W/Z+jet production at the LHC
hep-ph 2025-12 conditional novelty 6.0 of 10

Non-commutative spacetime corrections to W/Z+jet production appear at first order in Θ, and ATLAS Z+jet data constrain the non-commutative scale to Λ ≳ 2 TeV.
Entanglement through high-energy scattering in noncommutative quantum electrodynamics
hep-th 2025-06 conditional novelty 6.0 of 10

In noncommutative QED, tree-level photon and head-on fermion scattering with opposite helicities give the same concurrence as gluon scattering, maximal at a 90-degree scattering angle, while a right-angle fermion coll...
Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
hep-th 2006-03 conditional novelty 6.0 of 10

A consistency check shows the deformed-quantization approach to noncommutative field theory collapses to an ordinary commutative theory, so the claimed spin-statistics violation and disappearing UV/IR mixing are artifacts.
Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time
hep-th 2006-03 conditional novelty 6.0 of 10

Under the light-wedge causality of noncommutative QFT, the Jost-Lehmann-Dyson representation forces the amplitude's numerator to depend on the scattering angle, so no analyticity in cos Θ, and hence no Froissart-Marti...
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In 3D noncommutative electromagnetism, the Seiberg-Witten duality rule θ → ⋆θ g^2 holds only to second order and breaks at third order outside the slowly varying limit.
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Gauging a noneffectively-acting group yields a conformal field theory distinct from gauging its effective quotient, with extra twisted sectors describable as fields valued in roots of unity.
On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
hep-th 2004-08 accept novelty 6.0 of 10

Noncommutative spacetime with constant theta is invariant under a twist-deformed Poincaré Hopf algebra, which preserves the usual particle representation content and justifies Lorentz-covariant calculations in noncomm...
Top-quark pair production in electron-positron collisions within the minimal noncommutative Standard Model
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Noncommutative effects up to second order in Θ induce measurable deviations in the e+e− → tt̄ total cross section, polar and azimuthal distributions, and forward-backward asymmetry at ILC and CLIC energies.
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The paper claims microcausality holds for physical Dirac observables on noncommutative spacetime even though the underlying spinor bilinear Moyal commutator does not vanish.
Microcausality violation of scalar field on noncommutative spacetime with the time-space noncommutativity
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For a free scalar field on noncommutative spacetime, space-space noncommutativity preserves microcausality while time-space noncommutativity violates it, according to the author's Moyal-star-product calculation.
Schwinger Model In Noncommutating Space-Time
hep-th 2006-03 conditional novelty 5.0 of 10

For the noncommutative bosonized Schwinger model, the massive boson acquires, at first order in the noncommutativity parameter, an interaction with a background source, while unitarity and causality are claimed to persist.
Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling
hep-th 2026-05 unverdicted novelty 4.0 of 10

In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.
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How later papers used it

68 later papers cite it

Evidence: substantial. 68 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 25 of the 87 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

4 later papers by other authors are listed below: 4 cited it as support.

Cites it as support 4 of 7 papers with this label

Used this paper's result that nonzero θ^0i makes a noncommutative theory nonunitary to choose θ to lie in the (1, 2) plane without loss of generality.

Photon-neutrino interaction in theta-exact covariant noncommutative model: Phenomenology and Quantum properties* (2011) · 0.95 · paraphrased: the licence does not allow quoting
To circumvent potential unitarity issues associated with time-space or time-time non-commutativity [ref] , we restrict our analysis to the case of purely space-space non-commutativity.

Constraining non-commutative geometry with W/Z+jet production at the LHC (2025) · W/Z+jet phenomenology in NC geometry · 0.97
Chose the limit θ^0i = 0 since this paper shows the unitarity of the theory is violated for θ^0i ≠ 0.

Singlet scalar dark matter in the non-commutative space-time: a viable hypothesis to explain the gamma-ray excess in the galactic center (2020) · 0.97 · paraphrased: the licence does not allow quoting
In this work, we assume space-space non-commutativity, i.e., $Θ^i0 = 0$, motivated by unitarity considerations [ref] , and without loss of generality, we set $Θ^21 = Θ$ and $Θ^13 = Θ^23 = 0$.

Transverse momentum and rapidity distributions of top quarks in pair and single top quark production within the non-commutative standard model at the LHC (2024) · Top-Antitop Quark Production in the NC-SM · 0.99

How the literature uses it

64 arXiv papers cite this in 81 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

This S-matrix is manifestly unitary.

Unitarity in space-time noncommutative field theories · 0.99

Papers citing it · 63 sentences without a confident label

Cites it as support 5 papers

In fact it was shown in [ref] that in this case the modified Feynman rules lead to a violation of unitarity.

Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space · Introduction · 0.96
To circumvent potential unitarity issues associated with time-space or time-time non-commutativity [ref] , we restrict our analysis to the case of purely space-space non-commutativity.

Constraining non-commutative geometry with W/Z+jet production at the LHC · W/Z+jet phenomenology in NC geometry · 0.97
Since the unitarity of the theory is violated for $θ^0i≠0$ [ref] , the limit $θ^0i= 0$ is chosen.

Singlet scalar dark matter in the non-commutative space-time: a viable hypothesis to explain the gamma-ray excess in the galactic center · THE NCST THEORY · 0.97

Cites it as background 12 papers

We have three types of space-time noncommutativity [ref] : (i) The pure space-space (spacelike) NC, where $c_i0=0$; $c_ij≠0, ∀i,j=1,2,3$, makes unitary safe theory, (ii) the pure time-space (timelike) NC, with $c_i0≠0$; $c_ij=0, ∀i,j=1,2,3$, makes unitarity breaking theory, (iii) the so called lightlike noncommutativity satisfying $E^2_θ=B^2_θ$ and $E_θ ·B_θ=0$, where the $c_0i$ elements are defined by the direction of the background $E_θ=1/Λ_NC^2( c_01, c_02, c_03)$ field, while the $c_ij$ coefficients are defined by the direction of the $B_θ=1/Λ_NC^2 (c_23, -c_13, c_12)$ field, produces unitary safe NCQED theory.

Remarks on Compton forward scattering singularity in the NCQED · Compton scattering in the NCQED and collinear singularity · 0.80
The former case, discussed in Eq. [ref], encodes non-commutativity among space and time coordinates, namely $θ_0i≠0$, while the latter case, in Eq. [ref], corresponds to selecting $θ_0i=0$, ensuring unitarity of the $θ$-Poincaré models [ref] .

Strongest atomic physics bounds on Non-Commutative Quantum Gravity Models · Introduction · 0.81
We remark that noncommutative field theories typically contain infinitely many time derivatives in their actions, which may lead to apparent violations of unitarity [ref] and causality [ref] .

Exponentially Long Evaporation of Noncommutative Black Hole · Introduction · 0.84

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