Perturbative analysis on infrared aspects of noncommutative QED on R^4

M.Hayakawa

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Perturbative analysis on infrared aspects of noncommutative QED on R^4

M.Hayakawa

High Energy Physics - Theory · Submitted 12 Dec 1999

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

The authors' main claim The explicit calculation of the finite part of the photon vacuum polarization shows the singularity ln({q C^TC q}) (C^{\mu\nu} is a noncommutative parameter.) in the infrared side which also exists in noncommutative Yang-Mills theory.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.56 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Here we examine the noncommutative counterpart of QED, which is called as noncommutative QED. The theory is obtained by examining the consistent minimal coupling to noncommutative U(1) gauge field. The *-product admits the coupling of the matter with only three varieties of charges, i.e., 0, +1 and -1. Ultraviolet divergence can be absorbed into the rescaling of the fields and the parameters at least at one loop level. To examine the infrared aspect of the theory the anomalous magnetic dipole moment is calculated. The dependence on the direction of photon momentum reflects the Lorentz symmetry violation of the system. The explicit calculation of the finite part of the photon vacuum polarization shows the singularity ln({q C^TC q}) (C^{\mu\nu} is a noncommutative parameter.) in the infrared side which also exists in noncommutative Yang-Mills theory. It is associated with the ultraviolet behavior of the theory. We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only noncommutative QED.

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	Here we examine the noncommutative counterpart of QED, which is called as noncommutative QED.	contribution 0.62	0.54	0.03	asserted 0.98
s1	The theory is obtained by examining the consistent minimal coupling to noncommutative U(1) gauge field.	method 0.59	0.58	0.03	asserted 1.00
s2	The *-product admits the coupling of the matter with only three varieties of charges, i.e., 0, +1 and -1.	result 0.64	0.50	0.05	asserted 1.00
s3	Ultraviolet divergence can be absorbed into the rescaling of the fields and the parameters at least at one loop level.	result 0.99	0.69	0.10	asserted 0.61
s4	To examine the infrared aspect of the theory the anomalous magnetic dipole moment is calculated.	method 0.71	0.91	0.06	asserted 0.95
s5	The dependence on the direction of photon momentum reflects the Lorentz symmetry violation of the system.	interpretation 0.91	0.69	0.09	asserted 1.00
s6	The explicit calculation of the finite part of the photon vacuum polarization shows the singularity ln({q C^TC q}) (C^{\mu\nu} is a noncommutative parameter.) in the infrared side which also exists in noncommutative Yang-Mills theory.	result 1.00	0.89	0.37	asserted 1.00
s7	It is associated with the ultraviolet behavior of the theory.	interpretation 0.99	0.48	0.10	asserted 1.00
s8	We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only noncommutative QED.	result 0.47	0.78	0.16	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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The paper

Original abstract

Here we examine the noncommutative counterpart of QED, which is called as noncommutative QED. The theory is obtained by examining the consistent minimal coupling to noncommutative U(1) gauge field. The *-product admits the coupling of the matter with only three varieties of charges, i.e., 0, +1 and -1. Ultraviolet divergence can be absorbed into the rescaling of the fields and the parameters at least at one loop level. To examine the infrared aspect of the theory the anomalous magnetic dipole moment is calculated. The dependence on the direction of photon momentum reflects the Lorentz symmetry violation of the system. The explicit calculation of the finite part of the photon vacuum polarization shows the singularity ln({q C^TC q}) (C^{\mu\nu} is a noncommutative parameter.) in the infrared side which also exists in noncommutative Yang-Mills theory. It is associated with the ultraviolet behavior of the theory. We also consider the extension to chiral gauge theory in the present context, but the requirement of anomaly cancellation allows only noncommutative QED.

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References

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Cited by 6 Pith papers

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

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...
QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
hep-ph 2008-04 conditional novelty 6.0 of 10

Defining finite-volume QED without the zero-momentum photon modes removes the infrared pathology of periodic-box QED, and chiral perturbation theory then predicts that electromagnetic corrections to pseudoscalar meson...
Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories
hep-ph 2006-03 conditional novelty 6.0 of 10

Tree-level amplitudes in a Lorentz-invariant noncommutative field theory acquire a decaying form factor that suppresses cross sections above the noncommutative scale, distorts angular distributions, and removes the Co...
Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
astro-ph 2005-05 conditional novelty 6.0 of 10

Helicity-resolved effective-field-theory bookkeeping tightens some and weakens other astrophysical bounds on Planck-suppressed Lorentz violation, with photon decay in 50 TeV Crab gamma rays giving |eta| below about 0.2.
Quantum Electrodynamics on Noncommutative Spacetime
hep-th 2006-04 reject novelty 4.0 of 10

A proposal to quantize noncommutative U(1) gauge theory before Seiberg-Witten expansion, giving one-loop renormalizability and the ordinary QED value for the spin-dependent g-2.

Show 1 more citing papers

Quantum Field Theory on Noncommutative Spaces
hep-th 2001-09 accept novelty 2.0 of 10

The paper is a self-contained review that organizes noncommutative quantum field theory and its string-theoretic connections into a single pedagogical reference.

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56 later papers cite it

Evidence: substantial. 56 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

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1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 9 papers with this label

Found a vertex factor that is not symmetric under permutations of the legs and does not coincide with the vertex factor found in the modified Feynman rules of this paper.

Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism (2010) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

52 arXiv papers cite this in 76 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 · 45 sentences without a confident label

Uses its method or tool 1 paper

The commutation relation [ref] is implemented by use of the Weyl-Moyal star product and we take into account that the gauge group $U_⋆(1)$ is non-Abelian due to the star product [ref] .

Magnetic Monopoles in Noncommutative Space-Time: Second Order of Perturbation · Introduction · 0.81

Compares with it 9 papers

This is in agreement with the results obtained in [ref] in the setting of the modified Feynman rules, cf. ([ref],b).

Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space · The nonplanar part · 0.98
[equation] This is in agreement with the results obtained in [ref] in the setting of the modified Feynman rules, cf. ([ref],b).

Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism · The nonplanar part · 0.99
The structure in ([ref]) is different (it is NC-scale/energy dependent) with respect to the NC scale-independent structure from ([ref]), as well as to the structure arising from fermion self-energy computation in the case of $⋆$-product only unexpanded theories [ref] .

High energy cosmic rays experiments inspired by noncommutative quantum field theory · Discussion and conclusions · 1.00

Cites it as support 3 papers

We consider pure electrodynamics, i.e., we do not include fermionic matter fields[This can be justified by the fact that at $(e^2)$, the fermion contributions are exactly as in the commutative case [ref] and thus not of interest for our study.].

Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism · Introduction · 0.97
We consider pure electrodynamics, i.e., we do not include fermionic matter fields[This can be justified by the fact that at $(e^2)$, the fermion contributions are exactly as in the commutative case [ref] and thus not of interest for our study.].

Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space · The self–energy · 0.98
The reason, as in the naïve scalar case, is that one finds a quadratic IR divergence in the non-planar part of the self-energy (which is independent of the gauge fixing [ref] ).

On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review · Are non-commutative gauge theories feasible? · 0.99

Cites it as background 14 papers

For ordinary NC parameter, this theory is known to be one-loop renormalizable [ref] .

Nilpotent noncommutativity and renormalization · Noncommutative QED with bifermionic parameter · 0.81
There remains to discuss the origin of the singularity at $p̃^μ=0$ of the following contributions to $Γ_2[b^(0)]$ in ([ref]): [equation] The singular behaviour at $p̃^μ=0$ in the expression above comes uniquely from various types of integrals over $k$, all being given in Appendix B: [equation] The UV/IR mixing phenomenon that the latter integrals bring about has been amply discussed in the literature already [ref] .

UV/IR mixing in Noncommutative SU(N) Yang-Mills theory · The UV/IR mixing phenomenon · 0.93
Moving to NCST causes some problems such as charge quantization [ref] and gauge group definition [ref] .

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 · 0.91

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