Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term

Daniel N. Blaschke; Erwin Kronberger; Harald Grosse; Manfred Schweda; Michael Wohlgenannt

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Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term

Daniel N. Blaschke, Harald Grosse, Erwin Kronberger, Manfred Schweda, Michael Wohlgenannt

High Energy Physics - Theory · Submitted 18 Dec 2009

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The authors' main claim In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.

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arXiv ID0912.3642 (version 1)

Pith ID6EXXGB7C, Pith's permanent record of this paper and its review

CitationDaniel N. Blaschke, Erwin Kronberger, Harald Grosse, Manfred Schweda, Michael Wohlgenannt. "Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term." arXiv:0912.3642 (2009). https://pith.science/paper/6EXXGB7C

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.23 · mentions code or data availability 0.02.

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Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U(1) gauge field theory including an oscillator-like term in the action has been put forward in arXiv:0705.4205. The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U(1) gauge field theory including an oscillator-like term in the action has been put forward in arXiv:0705.4205.	background 0.98	0.11	0.03	asserted 1.00
s1	The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space.	contribution 0.87	0.22	0.04	hedged possibility 0.38
s2	In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.	contribution 0.55	0.94	0.07	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.66.

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Original abstract

Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U(1) gauge field theory including an oscillator-like term in the action has been put forward in arXiv:0705.4205. The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.

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17 arXiv papers cite this in 28 sentences

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Papers citing it · 16 sentences without a confident label

Uses its method or tool 2 papers

In order to find divergences and the form of counterterms we apply the method developed in [ref] : we amputate the leg of the tadpole, multiply it with the corresponding external field then and integrate.

Quantization of a gauge theory on a curved noncommutative space · Tadpoles: one-loop divergences · 1.00
This, in fact, was done in [ref] in order to calculate the graphs depicted in Fig. [ref].

Gauge Theories on Deformed Spaces · Extension to gauge theories · 0.88

Cites it as background 9 papers

Some significant progress on UV/IR mixing and related issues has been achieved [ref] while a proper understanding of loop corrections is still sought for.

Two-Point Functions on Deformed Spacetime · Introduction · 0.96
Some significant progress on UV/IR mixing and related issues has been achieved [ref] while a proper understanding of loop corrections is still sought for.

Self-energies on deformed spacetimes · Introduction · 0.83
Another, simplified version of a gauge model was discussed in [ref] .

Quantization of a gauge theory on a curved noncommutative space · Introduction · 0.92

What it cites · 30 sentences without a confident label

Builds on 1 paper

The current work mainly deals with loop calculations based on the previous letter [ref] , aiming to clarify whether the action we proposed there can lead to a renormalizable gauge theory.

Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry · Introduction · 0.85

Compares with 7 papers

Remarkably, these terms are present in the induced action calculated in Refs. [ref] .

Induced Gauge Theory on a Noncommutative Space · Tadpole graphs · 0.96
Remarkably, these terms are present in the induced action calculated in Refs. [ref] .

Noncommutative Induced Gauge Theory · Tadpole graphs · 0.96
We hence arrive at [equation] In the limit $→0$ (i.e. $ω→∞$) this expression reduces to the usual transversal term [equation] which is quadratically IR divergent[In fact, this term is consistent with previous results [ref] calculated in the “naïve” model, i.e. without any additional non-local terms in the action.] in the external momentum $p$ and logarithmically UV divergent.

Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry · Two point functions at one-loop level · 0.89

Cites as background 3 papers

One of the big challenges of the past decade has been the construction of renormalizable quantum field theories (QFTs) on space-time, usually plagued by the infamous problem [ref] .

Non-commutative Renormalization · Introduction · 0.99
One of the big challenges of the past decade has been the construction of renormalizable quantum field theories (QFTs) on space-time, usually plagued by the infamous problem [ref] .

Noncommutative Field Theory · Introduction · 0.99
One of the big challenges of the past decade has been the construction of renormalizable quantum field theories (QFTs) on space-time, usually plagued by the infamous problem [ref] .

Noncommutative Perturbative Dynamics · Introduction · 0.99

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