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Noncommutative Gravity Solutions
, 2009
"... We consider noncommutative geometries obtained from a triangular Drinfeld twist and review the formulation of noncommutative gravity. A detailed study of the abelian twist geometry is presented. Inspired by [1, 2], we obtain solutions of noncommutative Einstein equations by considering twists that a ..."
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We consider noncommutative geometries obtained from a triangular Drinfeld twist and review the formulation of noncommutative gravity. A detailed study of the abelian twist geometry is presented. Inspired by [1, 2], we obtain solutions of noncommutative Einstein equations by considering twists that are compatible with
Twisted noncommutative field theory with the Wick–Voros and Moyal products
 REV. D
"... We present a comparison of the noncommutative field theories built using two different star products: Moyal and WickVoros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic potential case, and calculate the Green’s functions up to one loo ..."
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We present a comparison of the noncommutative field theories built using two different star products: Moyal and WickVoros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic potential case, and calculate the Green’s functions up to one loop, for the two and four points cases. We compare the two theories in the context of the noncommutative geometry determined by a Drinfeld twist, and the comparison is made at the level of Green’s functions and Smatrix. We find that while the Green’s functions are different for the two theories, the Smatrix is
Cosmological and black hole spacetimes in twisted noncommutative gravity
 arXiv:0906.2730. A. Schenkel and C.F. Uhlemann
"... Abstract: We derive noncommutative Einstein equations for abelian twists and their solutions in consistently symmetry reduced sectors, corresponding to twisted FRW cosmology and Schwarzschild black holes. While some of these solutions must be rejected as models for physical spacetimes because they c ..."
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Abstract: We derive noncommutative Einstein equations for abelian twists and their solutions in consistently symmetry reduced sectors, corresponding to twisted FRW cosmology and Schwarzschild black holes. While some of these solutions must be rejected as models for physical spacetimes because they contradict observations, we find also solutions that can be made compatible with low energy phenomenology, while exhibiting strong
Škoda Z.: Exponential formulas and Lie algebra type star products
 SIGMA 8 (2012
"... Abstract. Given formal differential operators Fi on polynomial algebra in several variables x1,..., xn, we discuss finding expressions Kl determined by the equation exp( i xiFi)(exp( j qjxj)) = exp( lKlxl) and their applications. The expressions for Kl are related to the coproducts for deformed mom ..."
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Abstract. Given formal differential operators Fi on polynomial algebra in several variables x1,..., xn, we discuss finding expressions Kl determined by the equation exp( i xiFi)(exp( j qjxj)) = exp( lKlxl) and their applications. The expressions for Kl are related to the coproducts for deformed momenta for the noncommutative spacetimes of Lie algebra type and also appear in the computations with a class of star products. We find combinatorial recursions and derive formal differential equations for finding Kl. We elaborate an example for a Lie algebra su(2), related to a quantum gravity application from the literature. Key words: star product; exponential expression; formal differential operator 2010 Mathematics Subject Classification: 81R60; 16S30; 16S32; 16A58
QFT on homothetic Killing twist deformed curved spacetimes, Gen. Relativity Gravitation 43
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Translation invariance, commutation relations and ultraviolet/infrared mixing
"... We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the GrönewoldMoyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the ..."
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Cited by 4 (1 self)
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We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the GrönewoldMoyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the phase appearing in the nonplanar diagrams is the one given by the commutator of the coordinates, the semiclassical Poisson structure of the non commutative spacetime. We do this
Duality and Braiding in Twisted Quantum Field Theory,” arXiv:0711.1525 [hepth
"... We reexamine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green’s functions i ..."
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We reexamine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green’s functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states Twisted quantum field theory is a modification of the traditional approach to noncommutative field theory [19, 42] aimed at restoring the symmetries of spacetime which are broken by noncommutativity.
NONCOMMUTATIVE DIFFERENTIAL FORMS ON THE KAPPADEFORMED SPACE
, 812
"... Abstract. We construct a differential algebra of forms on the kappadeformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of oneforms and nilpotent exterior derivatives. We derive explicit expressions for the ..."
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Abstract. We construct a differential algebra of forms on the kappadeformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of oneforms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and oneforms in covariant and noncovariant realizations. We also introduce higherorder forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are not gradedcommutative, but they satisfy the graded Jacobi identity. The starproduct of classical differential forms is also defined. It is shown that the product depends on the realizations of both the noncommutative coordinates and oneforms on the kappadeformed space. 1.
The Structure of Spacetime and Noncommutative Geometry
, 2008
"... We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from commutative to noncommutative spaces. We then give a brief desc ..."
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We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from commutative to noncommutative spaces. We then give a brief description of Connes approach to the standard model, of the noncommutative geometry of strings and of field theory on noncommutative spaces. We also discuss the role of symmetries and some possible consequences for cosmology. Talk given at the workshop: Geometry, Topology, QFT and Cosmology, Paris, 2830 In this contribution I will give a general, and personal, overview of some attempts that physicists and mathematicians are making to understand the structure of spacetime at extremely small distances. The tool used for the description of spacetime at the Planck length scale is what is called Noncommutative
Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity
, 2009
"... We review the noncommutative gravity of Wess et al. [1, 2] and discuss its physical applications. We define noncommutative symmetry reduction and construct deformed symmetric solutions of the noncommutative Einstein equations. We apply our framework to find explicit deformed cosmological and black h ..."
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We review the noncommutative gravity of Wess et al. [1, 2] and discuss its physical applications. We define noncommutative symmetry reduction and construct deformed symmetric solutions of the noncommutative Einstein equations. We apply our framework to find explicit deformed cosmological and black hole solutions and discuss their phenomenology. This article is based on a joint work with Thorsten Ohl [3, 4]. 1.