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399
Exact solution of quantum field theory on noncommutative phase spaces
 017, 2004, hepth/0308043. – 43
"... We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the GroenewoldMoyal starproduct. Explicit results are presented for all Green’s fun ..."
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Cited by 59 (6 self)
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We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the GroenewoldMoyal starproduct. Explicit results are presented for all Green’s functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed nonperturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinitedimensional noncommutative algebra.
UV/IR mixing via closed strings and tachyonic instabilities
 Nucl. Phys. B
, 2002
"... We discuss UV/IR mixing effects in nonsupersymmetric non commutative U(N) gauge theories. We show that the singular (nonplanar) terms in the 2 and 3point functions, namely the poles and the logarithms, can be obtained from a manifestly gauge invariant effective action. The action, which involves ..."
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Cited by 38 (6 self)
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We discuss UV/IR mixing effects in nonsupersymmetric non commutative U(N) gauge theories. We show that the singular (nonplanar) terms in the 2 and 3point functions, namely the poles and the logarithms, can be obtained from a manifestly gauge invariant effective action. The action, which involves open Wilson line operators, can be derived from closed strings exchange between two stacks of Dbranes. Our concrete example is type 0B string theory and the field theory that lives on a collection of N electric D3branes. We show that one of the closed string modes that couple to the field theory operator Noncommutative gauge theories attracted recently a lot of attention, mainly due to the discovery of their relation to string/M theory [1, 2]. The perturbative dynamics of these theories is very interesting: planar graphs of noncommutative theories are exactly the same as the planar graphs of ordinary
Emergent Gravity and Noncommutative Branes from YangMills Matrix Models
, 2008
"... The framework of emergent gravity arising from YangMills matrix models is developed further, for general noncommutative branes embedded in R D. The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure an ..."
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Cited by 32 (17 self)
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The framework of emergent gravity arising from YangMills matrix models is developed further, for general noncommutative branes embedded in R D. The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure and the embedding metric in R D. A covariant form of the treelevel equations of motion is derived, and the Newtonian limit is discussed. This points to the necessity of branes in higher dimensions. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for a quantum theory of gravity coupled to matter. The Planck scale is then identified with the scale of N = 4 SUSY breaking. A mechanism for avoiding the cosmological constant
Noncommutative deformations of Wightman quantum field theories, JHEP 0809
, 2008
"... Abstract: Quantum field theories on noncommutative Minkowski space are studied in a modelindependent setting by treating the noncommutativity as a deformation of quantum field theories on commut ative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of i ..."
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Cited by 30 (3 self)
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Abstract: Quantum field theories on noncommutative Minkowski space are studied in a modelindependent setting by treating the noncommutativity as a deformation of quantum field theories on commut ative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its WeylWigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedgeshaped regions, and may therefore be used to compute noncommutative corrections to twoparticle Smatrix elements.
Twisting all the Way: from Classical Mechanics to Quantum Fields
, 2007
"... We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and sym ..."
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Cited by 29 (6 self)
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We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative spacetime, i.e. we establish a noncommutative correspondence principle from?Poisson brackets to?commutators. In particular commutation relations among creation and annihilation operators are deduced.
On the vacuum states for noncommutative gauge theory
, 2008
"... Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the ..."
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Cited by 27 (8 self)
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Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in the position space for these vacuum configurations in two and four dimensions.
Heatkernel approach to UV/IR mixing on isospectral deformation manifolds
"... We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) ‘quantum spaces’, generalizing Moyal planes and noncommutative tori, are constructed using Rieffel’s theory of deformation quantization by actions o ..."
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Cited by 27 (3 self)
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We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) ‘quantum spaces’, generalizing Moyal planes and noncommutative tori, are constructed using Rieffel’s theory of deformation quantization by actions of R l. Our framework, incorporating background field methods and tools of QFT in curved spaces, allows to deal both with compact and noncompact spaces, as well as with periodic and nonperiodic deformations, essentially in the same way. We compute the quantum effective action up to one loop for a scalar theory, showing the different UV/IR mixing phenomena for different kinds of isospectral deformations. The presence and behavior of the nonplanar parts of the Green functions is understood simply in terms of offdiagonal heat kernel contributions. For periodic deformations, a Diophantine condition on the noncommutivity parameters is found to play a role in the analytical nature of the nonplanar part of the oneloop reduced effective action. Existence of fixed points for the action may give rise to a new kind of UV/IR mixing. Keywords: noncommutative field theory, isospectral deformation, UV/IR mixing, heat kernel, Diophantine approximation.