The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
V. Putz - One of the best experts on this subject based on the ideXlab platform.
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No UV/IR mixing in unitary space-time non-Commutative Field theory
The European Physical Journal C, 2004Co-Authors: P. A. Fischer, V. PutzAbstract:In this article we calculate several divergent amplitudes in \(\phi^4\)-theory on non-Commutative space-time (\(\Theta_{0i} \neq 0\)) in the framework of interaction-point time-ordered perturbation theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules that allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the absence of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the Feynman rules we found, this opens promising vistas onto the systematic renormalization of non-Commutative Field theories.
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space time non Commutative Field theories and causality
European Physical Journal C, 2003Co-Authors: H Bozkaya, M Schweda, Harald Grosse, V. Putz, P Fischer, M Pitschmann, Raimar WulkenhaarAbstract:As argued previously, amplitudes of quantum Field theories on non-Commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-Commutative \(\phi^4\) theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only.
Subir Ghosh - One of the best experts on this subject based on the ideXlab platform.
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seiberg witten map and the axial anomaly in non Commutative Field theory
Physics Letters B, 2002Co-Authors: Rabin Banerjee, Subir GhoshAbstract:Abstract Using the point-splitting regularisation, we calculate the axial anomaly in an arbitrary even dimensional non-Commutative (NC) Field theory. Our result is (star) gauge invariant in its unintegrated form, to the leading order in the NC parameter. Exploiting the Seiberg–Witten map, this result gets transformed to the familiar Adler–Bell–Jackiw anomaly in ordinary spacetime. Furthermore, using this map, we derive an expression for the unintegrated axil anomaly for constant Fields in NC spacetime, that is valid to all finite orders of the NC parameter.
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Seiberg–Witten map and the axial anomaly in non-Commutative Field theory
Physics Letters B, 2002Co-Authors: Rabin Banerjee, Subir GhoshAbstract:Abstract Using the point-splitting regularisation, we calculate the axial anomaly in an arbitrary even dimensional non-Commutative (NC) Field theory. Our result is (star) gauge invariant in its unintegrated form, to the leading order in the NC parameter. Exploiting the Seiberg–Witten map, this result gets transformed to the familiar Adler–Bell–Jackiw anomaly in ordinary spacetime. Furthermore, using this map, we derive an expression for the unintegrated axil anomaly for constant Fields in NC spacetime, that is valid to all finite orders of the NC parameter.
Luis Alvarez-gaume - One of the best experts on this subject based on the ideXlab platform.
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General properties of non-Commutative Field theories
Nuclear Physics B, 2003Co-Authors: Luis Alvarez-gaume, Miguel Á. Vázquez-mozoAbstract:In this paper we study general properties of nonCommutative eld theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-eld. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with space-space noncommutativity. We analyze as well questions associated to the spin-statistics connections, and show that nonCommutative N = 4, U(1) gauge theory can be softly broken to N = 0 satisfying the axioms and providing an example where the Wilsonian low energy eective action can be constructed without UV/IR problems, after a judicious choice of soft breaking parameters is made. We also assess the phenomenological prospects of such a theory, which are in fact rather negative.
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Remarks on Time-Space NonCommutative Field Theories
Journal of High Energy Physics, 2001Co-Authors: Luis Alvarez-gaume, José L F Barbón, Roman ZwickyAbstract:We propose a physical interpretation of the perturbative breakdown of unitarity in time-like non-Commutative Field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closed-string modes. In this way, we give a unified view of the string-theoretical and the Field-theoretical no-go arguments against time-like non-Commutative theories. We also perform a quantitative study of various locality and causality properties of non-Commutative Field theories at the quantum level.
Vincent Rivasseau - One of the best experts on this subject based on the ideXlab platform.
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Renormalisation of non-Commutative Field theories
2009Co-Authors: Vincent Rivasseau, Fabien Vignes-tourneretAbstract:Very high energy physics needs a coherent description of the four fundamental forces. Non-Commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the classical level, thanks to the spectral action principle. Quantum Field theories on non-Commutative spaces is a first step towards the quantification of such a model. These theories can't be obtained simply by writing usual Field theory on non-Commutative spaces. Such attempts exhibit indeed a new type of divergencies, called ultraviolet/infrared mixing, which prevents renormalisability. H. Grosse and R. Wulkenhaar showed, with an example, that a modification of the propagator may restore renormalisability. This thesis aims at studying the generalization of such a method. We studied two different models which allowed to specify certain aspects of non-Commutative Field theory. In x space, the major technical difficulty is due to oscillations in the interaction part. We generalized the results of T. Filk in order to exploit such oscillations at best. We were then able to distinguish between two mixings, renormalizable or not. We also bring the notion of orientability to light : the orientable non-Commutative Gross-Neveu model is renormalizable without any modification of its propagator. The adaptation of multi-scale analysis to the matrix basis emphasized the importance of dual graphs and represents a first step towards a formulation of Field theory independent of the underlying space.
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Non Commutative Field Theory on Rank One Symmetric Spaces
arXiv: High Energy Physics - Theory, 2008Co-Authors: Pierre Bieliavsky, Razvan Gurau, Vincent RivasseauAbstract:Quantum Field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is taken to extend such theories to non-flat backgrounds such as solvable symmetric spaces.
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Why Renormalizable NonCommutative Quantum Field Theories?
2007Co-Authors: Vincent RivasseauAbstract:We complete our previous recent review on nonCommutative Field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy one can obtain an effective Commutative Field theory at lower energy.
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Renormalisation of non-Commutative Field theories
arXiv: High Energy Physics - Theory, 2007Co-Authors: Vincent Rivasseau, Fabien Vignes-tourneretAbstract:The first renormalisable quantum Field theories on non-Commutative space have been found recently. We review this rapidly growing subject.
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Non-Commutative Renormalization
Rigorous Quantum Field Theory, 2007Co-Authors: Vincent Rivasseau, Fabien Vignes-tourneretAbstract:We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non Commutative Field theory and suggest a related constructive program. This paper is dedicated to J. Bros on his 65th birthday.
Rabin Banerjee - One of the best experts on this subject based on the ideXlab platform.
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seiberg witten map and the axial anomaly in non Commutative Field theory
Physics Letters B, 2002Co-Authors: Rabin Banerjee, Subir GhoshAbstract:Abstract Using the point-splitting regularisation, we calculate the axial anomaly in an arbitrary even dimensional non-Commutative (NC) Field theory. Our result is (star) gauge invariant in its unintegrated form, to the leading order in the NC parameter. Exploiting the Seiberg–Witten map, this result gets transformed to the familiar Adler–Bell–Jackiw anomaly in ordinary spacetime. Furthermore, using this map, we derive an expression for the unintegrated axil anomaly for constant Fields in NC spacetime, that is valid to all finite orders of the NC parameter.
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Seiberg–Witten map and the axial anomaly in non-Commutative Field theory
Physics Letters B, 2002Co-Authors: Rabin Banerjee, Subir GhoshAbstract:Abstract Using the point-splitting regularisation, we calculate the axial anomaly in an arbitrary even dimensional non-Commutative (NC) Field theory. Our result is (star) gauge invariant in its unintegrated form, to the leading order in the NC parameter. Exploiting the Seiberg–Witten map, this result gets transformed to the familiar Adler–Bell–Jackiw anomaly in ordinary spacetime. Furthermore, using this map, we derive an expression for the unintegrated axil anomaly for constant Fields in NC spacetime, that is valid to all finite orders of the NC parameter.