Divergences in QFT on the Noncommutative Minkowski Space with Grosse-Wulkenhaar potential

Jochen Zahn

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Divergences in QFT on the Noncommutative Minkowski Space with Grosse-Wulkenhaar potential

Jochen Zahn

High Energy Physics - Theory · Submitted 3 May 2011

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

The authors' main claim This shows that we do not deal with an ordinary ultraviolet divergence.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.87 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.11 · mentions code or data availability 0.02.

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We study quantum field theory on the two-dimensional Noncommutative Minkoswki space with a Grosse-Wulkenhaar potential. We explicitly construct the retarded propagator and show that it is not a tempered distribution. This leads to problems when trying to define planar products of such distributions, as they appear in the Yang-Feldman series. At and above the self-dual point, these can no longer be defined, not even at different points. This shows that we do not deal with an ordinary ultraviolet divergence.

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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 quantum field theory on the two-dimensional Noncommutative Minkoswki space with a Grosse-Wulkenhaar potential.	contribution 0.73	0.82	0.04	asserted 0.84
s1	We explicitly construct the retarded propagator and show that it is not a tempered distribution.	result 0.66	0.96	0.19	asserted 1.00
s2	This leads to problems when trying to define planar products of such distributions, as they appear in the Yang-Feldman series.	interpretation 0.84	0.61	0.09	asserted 0.89
s3	At and above the self-dual point, these can no longer be defined, not even at different points.	result 0.95	0.82	0.26	asserted 1.00
s4	This shows that we do not deal with an ordinary ultraviolet divergence.	interpretation 0.98	0.86	0.43	asserted 1.00

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

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The paper

Original abstract

We study quantum field theory on the two-dimensional Noncommutative Minkoswki space with a Grosse-Wulkenhaar potential. We explicitly construct the retarded propagator and show that it is not a tempered distribution. This leads to problems when trying to define planar products of such distributions, as they appear in the Yang-Feldman series. At and above the self-dual point, these can no longer be defined, not even at different points. This shows that we do not deal with an ordinary ultraviolet divergence.

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What it cites · 16 sentences without a confident label

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The definition of the $$-product of distributions at different points can be done by duality, as proposed in [ref] : [equation] As the $$-product at coinciding points [ref], the $$-product at different points is best defined in momentum space, i.e., [equation] Using [ref], we obtain [equation] As the retarded propator is an element of $'_α, A(^4)$, it is natural to expect that the two-point function $Δ_+$ also lies in a subspace of that space.

Star product algebras of test functions · The planar divergence · 0.98
As an approach that does not share this problem, quantization in the Yang-Feldman formalism was proposed in [ref] , and this is the way we proceed here.

On the unitarity problem in space/time noncommutative theories · Introduction · 0.96
The problems connected to the $$-product and the distributional character of the propagators can be disentagled in the following way[In [ref] , this strategy was pursued for the definition of quasiplanar Wick products.]: In a first step, one defines the $$-product at different points.

Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products · The planar divergence · 0.91

Cites as support 1 paper

Thus, also in this setting, one finds a divergence in planar diagrams at the self-dual point [ref] .

Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential · The planar divergence · 0.96

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