Physical Instances of Noncommuting Coordinates

R. Jackiw

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Physical Instances of Noncommuting Coordinates

R. Jackiw

High Energy Physics - Theory · Submitted 5 Oct 2001

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

The authors' main claim Noncommuting spatial coordinates and fields can be realized in actual physical situations.

how it is stated · asserted 0.78 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, 2,203 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.57 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).

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	Noncommuting spatial coordinates and fields can be realized in actual physical situations.	result 0.42	0.31	0.62	asserted 0.78
s1	Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).	result 0.90	0.50	0.31	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.81.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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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

Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).

Human review

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References

Forward citations

Cited by 3 Pith papers

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

The Standard Model on Non-Commutative Space-Time
hep-ph 2001-11 accept novelty 6.0 of 10

Expanding the Standard Model on non-commutative space-time to first order in theta yields new quark-gluon-electroweak vertices, parity violation in non-commutative QCD, and an unmodified photon sector in the minimal c...
Composite Dark Matter with Invisible Light from Almost-Commutative Geometry
astro-ph 2006-03 conditional novelty 5.0 of 10

A noncommutative-geometry dark matter model with doubly charged leptons and a new U(1) force is shown, through a series of estimates, to avoid the anomalous-helium overproduction problem.
Lectures on Fuzzy and Fuzzy SUSY Physics
hep-th 2005-11 conditional novelty 3.0 of 10

The notes compile and explain fuzzy sphere and fuzzy supersphere constructions, star products, gauge fields, Dirac operators, anomalies, and exact fuzzy supersymmetry.

How the literature uses it

18 arXiv papers cite this in 19 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 citing it · 10 sentences without a confident label

Cites it as support 1 paper

In the ultra-strong magnetic regime, the kinetic energy becomes negligible, and its effects are entirely suppressed [ref] .

Magnetically Induced Schr\"odinger Cat States: The Shadow of a Quantum Space · Two-Particle System: Classical picture · 0.96

Cites it as background 8 papers

The classic textbook example [ref] of the quantum Landau problem has remained a constant source of fascination and inspiration [ref] , in fields apparently so diverse as two dimensional collective quantum fermionic systems [ref] , the search towards a fundamental unification of gravity with the other quantum interactions, or noncommutative deformation quantisation of geometries [ref] .

Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane · Introduction · 0.98
The idea of noncommutativity in the coordinates of spacetime can be attributed to Heisenberg [ref] , and it was subsequently developed further by Snyder [ref] as a means to address the issue of divergences in quantum field theory.

Quantization of Length in Spaces with Position-Dependent Noncommutativity · Introduction · 0.99
It was only in 1947, with Snyder [ref] , that this idea of space-time non-commutativity was formalized (for a historical introduction, see [ref] ).

Free-fall in a uniform gravitational field in non-commutative quantum mechanics · Introduction · 1.00

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