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On the Problem of Renormalizability in NonCommutative Gauge Field Models — A Critical Review
"... When considering quantum field theories on noncommutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe noncommutative scalar field theories on fourdimensional Euclidean GroenewoldMoyal deformed space ..."
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When considering quantum field theories on noncommutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe noncommutative scalar field theories on fourdimensional Euclidean GroenewoldMoyal deformed space, also known as ‘θdeformed space ’ R4 θ. In this work we discuss some major obstacles of constructing a renormalizable noncommutative gauge field model and sketch some possible ways out. 1
Improved localization of a renormalizable noncommutative translation invariant U(1) gauge model, Europhys
 Lett
"... Motivated by the recent work of Vilar et al. [1] we enhance our noncommutative translation invariant gauge model [2] by introducing auxiliary fields and ghosts forming a BRST doublet structure. In this way localization of the problematic 1 D2 term can be achieved without the necessity for any addit ..."
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Motivated by the recent work of Vilar et al. [1] we enhance our noncommutative translation invariant gauge model [2] by introducing auxiliary fields and ghosts forming a BRST doublet structure. In this way localization of the problematic 1 D2 term can be achieved without the necessity for any additional degrees of freedom. The resulting theory is suspected to be renormalizable. A rigorous proof, however, has not been accomplished up to now. 1
Oneloop calculations and detailed analysis of the localized noncommutative p −2 U(1) gauge model
 Vilar L.C.Q., Ventura O.S., Tedesco D.G., Lemes V.E.R., Renormalizable
, 804
"... doi:10.3842/SIGMA.2010.037 Abstract. This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θdeformed noncommutative 1 p2 model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009), 275–290]. It is shown that breaking terms ..."
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Cited by 3 (1 self)
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doi:10.3842/SIGMA.2010.037 Abstract. This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θdeformed noncommutative 1 p2 model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009), 275–290]. It is shown that breaking terms of the form used by Vilar et al. [J. Phys. A: Math. Theor. 43 (2010), 135401, 13 pages] and ourselves [Eur. Phys. J. C: Part. Fields 62 (2009), 433–443] to localize the BRST covariant operator ( D2θ2D 2) −1 lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit oneloop calculations, and analyze the mechanism the mentioned problems originate from. Key words: noncommutative field theory; gauge field theories; renormalization 2010 Mathematics Subject Classification: 81T13; 81T15; 81T75 1
On the Development of NonCommutative TranslationInvariant Quantum Gauge Field Models
, 2009
"... Aiming to understand the most fundamental principles of nature one has to approach the highest possible energy scales corresponding to the smallest possible distances – the Planck scale. Historically, three different theoretical fields have been developed to treat the problems appearing in this ende ..."
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Cited by 2 (1 self)
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Aiming to understand the most fundamental principles of nature one has to approach the highest possible energy scales corresponding to the smallest possible distances – the Planck scale. Historically, three different theoretical fields have been developed to treat the problems appearing in this endeavor: string theory, quantum gravity, and noncommutative (NC) quantum field theory (QFT). The latter was originally motivated by the conjecture that the introduction of uncertainty relations between spacetime coordinates introduces a natural energy cutoff, which should render the resulting computations well defined and finite. Despite failing to fulfill this expectation, NC physics is a challenging field of research, which has proved to be a fruitful source for new ideas and methods. Mathematically, noncommutativity is implemented by the so called Weyl quantization, giving rise to a modified product — the GroenewoldMoyal product. It realizes an operator ordering, and allows to work within the well established framework of QFT on noncommutative spaces. The main obstacle of NCQFT is the appearance of singularities being shifted from high to low energies. This effect, being referred to as ‘UV/IR mixing’, is a direct consequence of the de
On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2010
"... The harmonic term in the scalar field theory on the Moyal space removes the UVIR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the Langmann–Szabo duality, the superalgebraic approach and the noncommuta ..."
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The harmonic term in the scalar field theory on the Moyal space removes the UVIR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the Langmann–Szabo duality, the superalgebraic approach and the noncommutative scalar curvature interpretation. Then, we show some deep relationship between these interpretations.
Gauge Theories on Deformed Spaces
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2010
"... The aim of this review is to present an overview over available models and approaches to noncommutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold–Moyal spaces and renormalizability, but we will also review other deformations and try to point out common fe ..."
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The aim of this review is to present an overview over available models and approaches to noncommutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold–Moyal spaces and renormalizability, but we will also review other deformations and try to point out common features. This review will by no means be complete and cover all approaches, it rather reflects a highly biased selection.
InDepth Analysis of the Localized NonCommutative p −2 U(1) Gauge Model
, 2009
"... This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θdeformed noncommutative 1 p2 model originally introduced by Gurau et al. [1]. It is shown that breaking terms of the form used by Vilar et al. [2] and ourselves [3] to localize the BR ..."
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This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θdeformed noncommutative 1 p2 model originally introduced by Gurau et al. [1]. It is shown that breaking terms of the form used by Vilar et al. [2] and ourselves [3] to localize the BRST covariant operator ( D2θ2D2) −1 lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit oneloop calculations, and analyze the mechanism
BPHZ renormalization and its application to noncommutative
, 2013
"... field theory ..."
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