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Deformations of quantum field theories and integrable models
 Comm. Math. Phys
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Dirac field on Moyal–Minkowski spacetime and noncommutative potential scattering
 Comm. Math. Phys
"... on the occasion of his 61st birthday Abstract. The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyaldeformed multiplication with respect to the ..."
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Cited by 10 (2 self)
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on the occasion of his 61st birthday Abstract. The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyaldeformed multiplication with respect to the spatial variables. The Moyaldeformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spectral geometry. It will be explained how this leads to an interpretation of the Dirac field as a quantum field theory on Moyaldeformed Minkowski spacetime (with commutative time) in a setting of Lorentzian spectral geometries of which some basic aspects will be sketched. The scattering transformation will be shown to be unitarily implementable in the canonical vacuum representation of the Dirac field. Furthermore, it will be indicated how the functional derivatives of the ensuing unitary scattering operators with respect to the strength of the noncommutative potential induce, in the spirit of Bogoliubov’s formula, quantum field operators (corresponding to observables) depending on the elements of the noncommutative algebra of MoyalMinkowski spacetime. 1
Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model,”Commun
 Math. Phys
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Deformations of quantum field theories on spacetimes with Killing vector fields,” arXiv:1006.3548 [mathph
"... Abstract. The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedgelike regions which share the essential causal properties of the Poincaré transforms of the Rindler we ..."
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Cited by 9 (1 self)
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Abstract. The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedgelike regions which share the essential causal properties of the Poincaré transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied. 1
Deformations of quantum field theories on de Sitter spacetime
 J. Math. Phys
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on spacetimes with Killing vector fields
"... Abstract. The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedgelike regions which share the essential causal properties of the Poincaré transforms of the Rindler wed ..."
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Abstract. The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedgelike regions which share the essential causal properties of the Poincaré transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied. 1
TwoPoint Functions on Deformed Spacetime?
, 2014
"... Abstract. We present a review of the oneloop photon (Π) and neutrino (Σ) twopoint functions in a covariant and deformed U(1) gaugetheory on the 4dimensional noncommutative spaces, determined by a constant antisymmetric tensor θµν, and by a parameterspace (κf, κg), respectively. For the general ..."
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Abstract. We present a review of the oneloop photon (Π) and neutrino (Σ) twopoint functions in a covariant and deformed U(1) gaugetheory on the 4dimensional noncommutative spaces, determined by a constant antisymmetric tensor θµν, and by a parameterspace (κf, κg), respectively. For the general fermionphoton Sf (κf) and photon selfinteraction Sg(κg) the closed form results reveal twopoint functions with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(µ2(θp)2). In addition, the photonloop produces new tensor structures satisfying transversality condition by themselves. We show that the photon twopoint function in the 4dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of θµν and setting deformation parameters (κf, κg) = (0, 3). In this case the neutrino twopoint function vanishes. Thus for a specific point (0, 3) in the parameterspace (κf, κg), a covariant θexact approach is able to produce a divergencefree result for the oneloop quantum corrections, having also both welldefined commutative limit and pointlike limit of an extended object. Key words: noncommutative geometry; photon and neutrino physics; nonperturbative effects 2010 Mathematics Subject Classification: 81R60; 81T10; 81T15 1
Gauge Theories on Deformed Spaces
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2010
"... The aim of this review is to present an overview over available models and approaches to noncommutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold–Moyal spaces and renormalizability, but we will also review other deformations and try to point out common fe ..."
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The aim of this review is to present an overview over available models and approaches to noncommutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold–Moyal spaces and renormalizability, but we will also review other deformations and try to point out common features. This review will by no means be complete and cover all approaches, it rather reflects a highly biased selection.