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On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach
High Energy Physics - Theory · Submitted 17 Feb 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.
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The abstract, sentence by sentence
We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{{}{D}^{2}}{F}_{\mu \nu}\ast \frac{1}{{}{D}^{2}}{F}^{\mu \nu}$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\textbf{C62}:433-443,2009)$. We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{{}{D}^{2}}{F}_{\mu \nu}\ast \frac{1}{{}{D}^{2}}{F}^{\mu \nu}$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. | contribution 0.99 | 0.69 | 0.07 | asserted 0.65 |
| s1 | Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. | background 1.00 | 0.04 | 0.03 | asserted 0.97 |
| s2 | More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\textbf{C62}:433-443,2009)$. | background 1.00 | 0.09 | 0.03 | asserted 1.00 |
| s3 | We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. | method 0.60 | 0.49 | 0.14 | asserted 0.93 |
| s4 | This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT. | method 0.62 | 0.47 | 0.17 | asserted 0.73 |
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The paper
Original abstract
We investigate the quantum effects of the nonlocal gauge invariant operator $\frac{1}{{}{D}^{2}}{F}_{\mu \nu}\ast \frac{1}{{}{D}^{2}}{F}^{\mu \nu}$ in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out $(Eur.Phys.J.\textbf{C62}:433-443,2009)$. We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to make a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.
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How the literature uses it
14 arXiv papers cite this in 32 sentences
Papers citing it · 26 sentences without a confident label
Builds on it 1 paper
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Following the ideas of Vilar [ref] , the localized action [ref] was further developed in [ref] by replacing $_$ with a complex conjugated pair of fields ($B_$, $_$) and by the introduction of an additional pair of ghost and antighost fields $ψ_$ and $_$ (all of mass dimension 1), thus leading to [equation] In this expression, as well as throughout the remainder of this section, all field products are considered to be star products.
One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model · Review: the construction of the model · 0.86
Uses its method or tool 2 papers
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Motivated by the work of Vilar [ref] we have eliminate the non-local terms with the help of auxiliary fields forming BRST-doublet structures [ref] : Γ^(0) = ∫d^4x ( 1/4 F_μν F_μν + λ/2 ( B_μν + B̅_μν) F_μν . . - μ^2 B̅_μν⋆D^2 D^2 B_μν + μ^2 ψ̅D^2 D^2 ψ) .
On NCQFT and dimensionless insertions · $U(1)$ Gauge theory · 0.88
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It is partly based on [ref] where a clever adaptation of the Zwanziger method [ref] of localization of non-local action for QCD is applied to noncommutative gauge theory on Moyal space.
Gauge theories on quantum spaces · $1/p^2$1/p3̂ gauge models and IR damping. · 0.82
Cites it as background 3 papers
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Thus, the action has to be modified and, inspired by the results achieved for the scalar models, various approaches have been proposed in recent years [ref] – see also the discussion [ref] and references therein.
BPHZ renormalization and its application to non-commutative field theory · Non-commutative gauge field theories · 0.80
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Inspired by the results achieved for the scalar models, various approaches have been proposed in recent years [ref] — see also the discussion [ref] and references therein.
Gauge Fields on Non-Commutative Spaces and Renormalization · Non-commutative gauge field theories · 0.84
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Various approaches to implementing a damping mechanism similar to the scalar $1/p^2$-model were also discussed — see [ref] .
Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences · Introduction · 0.94
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