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15
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 ..."
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Cited by 53 (16 self)
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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.
Noncommutative Induced Gauge Theory
, 2007
"... We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4dimensional Moyal space and compute in position space the oneloop YangMillstype effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action ..."
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Cited by 38 (10 self)
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We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4dimensional Moyal space and compute in position space the oneloop YangMillstype effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure YangMills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative ϕ 4theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.
Noncommutative Induced Gauge Theories on Moyal Spaces
, 2007
"... Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, ..."
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Cited by 13 (4 self)
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Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4D of the oneloop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure YangMills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ϕ 4theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed.
Derivations of the Moyal Algebra and Noncommutative Gauge Theories
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2009
"... The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital a ..."
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Cited by 12 (3 self)
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The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of Z2graded unital involutive algebras. We show, in the case of the Moyal algebra or some related Z2graded version of it, that the derivation based differential calculus is a suitable framework to construct Yang–Mills–Higgs type models on Moyal (or related) algebras, the covariant coordinates having in particular a natural interpretation as Higgs fields. We also exhibit, in one situation, a link between the renormalisable NC ϕ4model with harmonic term and a gauge theory model. Some possible consequences of this are briefly discussed.
Examples of derivationbased differential calculi related to noncommutative gauge theories
 INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
, 2008
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Heat Trace Asymptotics on Noncommutative Spaces
, 2007
"... This is a minireview of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered. ..."
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Cited by 6 (4 self)
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This is a minireview of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
Gauge theories in noncommutative geometry
, 2011
"... In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and gauge transformations. Two different approaches to noncommut ..."
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Cited by 2 (2 self)
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In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and gauge transformations. Two different approaches to noncommutative geometry are covered: the one based on derivations and the one based on spectral triples. Examples of noncommutative gauge field theories are given to illustrate the constructions and to display some of the common features.
deformed
, 2006
"... Differential calculus and gauge transformations on a ..."
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Cited by 1 (0 self)
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Differential calculus and gauge transformations on a
Strong field, noncommutative QED
, 2010
"... We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of consta ..."
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We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of constant backgrounds by giving a new and revealing interpretation of the photon dispersion relation. Considering scattering in background fields, we then show that the noncommutative photon is primarily responsible for generating deviations from strong field QED results. Finally, we propose a new method for constructing gauge invariant variables in noncommutative QED, and use it to analyse the physics of our null background fields.
Preprint ESI 1971 (2007) Induced Gauge Theory on a Noncommutative Space 1
, 804
"... Abstract. We discuss the calculation of the 1loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar φ 4 model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior g ..."
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Abstract. We discuss the calculation of the 1loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar φ 4 model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge field to the scalar field and extract the dynamics for the gauge field from the divergent terms of the 1loop effective action using a matrix basis. This results in proposing an action for noncommutative gauge theory, which is a candidate for a renormalisable model. PACS numbers: 11.10.Nx, 11.15.q 1.