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169
Selfdual noncommutative φ4theory in four dimensions is a nonperturbatively solvable and nontrivial quantum field theory,” arXiv:1205.0465
"... in four dimensions is a nonperturbatively solvable and nontrivial quantum field theory ..."
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in four dimensions is a nonperturbatively solvable and nontrivial quantum field theory
Oneloop calculations for a translation invariant noncommutative gauge model
 Eur. Phys. J. C
"... In this paper we discuss oneloop results for the translation invariant noncommutative gauge field model we recently introduced in ref. [1]. This model relies on the addition of some carefully chosen extra terms in the action which mix long and short scales in order to circumvent the infamous UV/IR ..."
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Cited by 18 (12 self)
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In this paper we discuss oneloop results for the translation invariant noncommutative gauge field model we recently introduced in ref. [1]. This model relies on the addition of some carefully chosen extra terms in the action which mix long and short scales in order to circumvent the infamous UV/IR mixing, and were motivated by the renormalizable noncommutative scalar model of Gurau et al. [2].
Interacting Fermi liquid in two dimensions at finite temperature, Part II: Renormalization
"... Using the method of continuous renormalization group around the Fermi surface, we prove that a twodimensional interacting system of Fermions at low temperature T remains a Fermi liquid (analytic in the coupling constant λ) for λ ≤ c/  log T  where c is some numerical constant. This bound is a ste ..."
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Using the method of continuous renormalization group around the Fermi surface, we prove that a twodimensional interacting system of Fermions at low temperature T remains a Fermi liquid (analytic in the coupling constant λ) for λ ≤ c/  log T  where c is some numerical constant. This bound is a step in the program of rigorous (nonperturbative) study of the BCS phase transition for many Fermions systems; it proves in particular that in dimension two the transition temperature (if any) must be nonperturbative in the coupling constant. The proof is organized into two parts: the present paper deals with the convergent contributions, and a companion paper (Part II) deals with the renormalization of dangerous two point subgraphs and achieves the proof. I
NonCommutative Complete Mellin Representation for Feynman Amplitudes,” arXiv:0705.3437 [mathph
"... We extend the complete Mellin (CM) representation of Feynman amplitudes to the noncommutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy of Feynman amplitudes in parameters such as the dimension of spacetime. In particular it paves the ..."
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We extend the complete Mellin (CM) representation of Feynman amplitudes to the noncommutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy of Feynman amplitudes in parameters such as the dimension of spacetime. In particular it paves the road for the dimensional renormalization of these theories. This complete Mellin representation also allows the study of asymptotic behavior under rescaling of arbitrary subsets of external invariants of any Feynman amplitude. 1
From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
, 707
"... This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not received the attention it actually deserves. T ..."
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This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not received the attention it actually deserves. The unifying concept for convergence acceleration methods is that in many cases, one can reach much faster convergence than by adding a particular series term by term. In some cases, it is even possible to use a divergent input series, together with a suitable sequence transformation, for the construction of numerical methods that can be applied to the calculation of special functions. This review both aims to provide some practical guidance as well as a groundwork for the study of specialized literature. As a second topic, we review some recent developments in the field of Borel resummation, which is generally recognized as one of the most versatile methods for the summation of factorially divergent (perturbation) series. Here, the focus is on algorithms which make optimal use of all information contained in a finite set of perturbative coefficients. The unifying concept for the various aspects of the Borel method investigated here is
Constructive Matrix Theory
, 2008
"... We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a nonperturbative construction of the φ ⋆4 4 field theory on the Moyal four dimensional space. 1 ..."
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We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a nonperturbative construction of the φ ⋆4 4 field theory on the Moyal four dimensional space. 1
Feynman diagrams in algebraic combinatorics, Séminaire Lotharingien de Combinatoire 49
 2002–04), Article B49c, 45 pp. SPECIES AND FEYNMAN DIAGRAMS 37
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Continuous Constructive Fermionic Renormalization
 Annales Henri Poincaré
"... Abstract We build the two dimensional GrossNeveu model by a new method which requires neither cluster expansion nor discretization of phasespace. It simply reorganizes the perturbative series in terms of trees. With this method we can for the first time define non perturbatively the renormalizatio ..."
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Abstract We build the two dimensional GrossNeveu model by a new method which requires neither cluster expansion nor discretization of phasespace. It simply reorganizes the perturbative series in terms of trees. With this method we can for the first time define non perturbatively the renormalization group differential equations of the model and at the same time construct explicitly their solution. I
Noncommutative QFT and Renormalization
, 2006
"... Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to φ 3 models and use the heat kernel ..."
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Cited by 15 (5 self)
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Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to φ 3 models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a θdeformed space and derive noncommutative gauge field actions.