Results 1  10
of
174
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
Abstract

Cited by 397 (26 self)
 Add to MetaCart
(Show Context)
A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
Comments on Perturbative Dynamics of Noncommutative YangMills Theory
 Nucl. Phys. B
"... We study the U(N) noncommutative YangMills theory at the oneloop approximation. We check renormalizability and gauge invariance of the model and calculate the oneloop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency che ..."
Abstract

Cited by 104 (5 self)
 Add to MetaCart
(Show Context)
We study the U(N) noncommutative YangMills theory at the oneloop approximation. We check renormalizability and gauge invariance of the model and calculate the oneloop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the θ → 0 limit of the U(N) theory does not converge to the ordinary SU(N) × U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing. 1 Introduction and Conclusions Noncommutative gauge field theories lately attracted a lot of attention, mainly due to the discoveries of their relation to string theory [1]. It was also found that the perturbative structure of these theories has an interesting pattern. It was shown [2], in the case of scalar theory, that planar
Enveloping algebra valued gauge transformations for nonabelian gauge groups on noncommutative spaces
, 2000
"... ..."
Nonabelian noncommutative gauge theory via noncommutative extra dimensions
, 2001
"... The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arise in string theory with background Bfields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discus ..."
Abstract

Cited by 68 (10 self)
 Add to MetaCart
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arise in string theory with background Bfields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich’s formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (SeibergWitten map.) As application we show the exact equality of the DiracBornInfeld action with Bfield in the commutative setting and its seminoncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups.
The standard model on noncommutative spacetime
 PHYS. J. C23
"... We consider the Standard Model on a noncommutative space and expand the action in the noncommutativity parameter θ µν. No new particles are introduced, the structure group is SU(3) × SU(2) × U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard ..."
Abstract

Cited by 62 (5 self)
 Add to MetaCart
We consider the Standard Model on a noncommutative space and expand the action in the noncommutativity parameter θ µν. No new particles are introduced, the structure group is SU(3) × SU(2) × U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in θ µν we find new vertices which are absent in the Standard Model on commutative spacetime. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in noncommutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the
Emergent Gravity from Noncommutative Gauge Theory
, 2007
"... We show that the matrixmodel action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, which is determined by a dyn ..."
Abstract

Cited by 61 (29 self)
 Add to MetaCart
We show that the matrixmodel action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to recover e.g. the Newtonian limit with arbitrary mass distribution. It also suggests a consistent picture of UV/IR mixing in terms of an induced gravity action. This should provide a suitable framework for quantizing gravity.
Induced Gauge Theory on a Noncommutative Space
, 2007
"... We consider a scalar φ4 theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field fr ..."
Abstract

Cited by 53 (16 self)
 Add to MetaCart
We consider a scalar φ4 theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.
Gauge and Einstein gravity from nonabelian gauge models on noncommutative spaces, Phys. Lett. B498 (2001) 74, hepth/0009163
 Rev
"... Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding Seiber–Witten maps are established which allow the definition of ..."
Abstract

Cited by 31 (20 self)
 Add to MetaCart
(Show Context)
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding Seiber–Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.
The energymomentum tensor on noncommutative spaces: Some pedagogical comments
, 2000
"... Abstract. We present the discussion of the energymomentum tensor of the scalar φ4theory on a noncommutative space. The Noether procedure is performed at the operator level. Additionally, the broken dilatation symmetry will be considered in a MoyalWeyl deformed scalar field theory at the classical ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We present the discussion of the energymomentum tensor of the scalar φ4theory on a noncommutative space. The Noether procedure is performed at the operator level. Additionally, the broken dilatation symmetry will be considered in a MoyalWeyl deformed scalar field theory at the classical level. 2 Work supported by The Danish Research Agency.