Noncommutative Field Theories from a Deformation Point of View

Waldmann, Stefan

doi:10.1007/978-3-7643-8736-5_7

Cited by 2 publications

(1 citation statement)

References 36 publications

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“…[32][33][34][35][36], are discussed and developed further in the physics literature. They seem to give promising models for gauge theories on noncommutative space-times, see also [44] for a review on the geometric nature of such noncommutative field theories.…”

Section: Introductionmentioning

confidence: 99%

Deformation quantization of surjective submersions and principal fibre bundles

Bordemann¹,

Neumaier²,

Waldmann³

et al. 2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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In this paper we establish a notion of deformation quantization of a surjective submersion which is specialized further to the case of a principal fibre bundle: the functions on the total space are deformed into a right module for the star product algebra of the functions on the base manifold. In case of a principal fibre bundle we require in addition invariance under the principal action. We prove existence and uniqueness of such deformations. The commutant within all differential operators on the total space is computed and gives a deformation of the algebra of vertical differential operators. Applications to noncommutative gauge field theories and phase space reduction of star products are discussed. * Martin.Bordemann@uha.fr ‡

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Section: Introductionmentioning

confidence: 99%

Deformation quantization of surjective submersions and principal fibre bundles

Bordemann¹,

Neumaier²,

Waldmann³

et al. 2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

Self Cite

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On a connection with a torsion non-tensor and a curvature non-tensor

Polyakova

2022

Differ. Geom. Mnogoobr. Figur

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This paper relates to differential geometry, and the research technique is based on G. F. Laptev’s method of extensions and envelopments, which generalizes E. Cartan's method of moving frame and exterior forms. A manifold is studied, the structure equations and derivational formulas of which are built using the deformations of the exterior and ordinary differentials. The manifold in question is a deformation of an ordinary smooth manifold. The bundles of non-symmetrical coframes and frames of the second order on this manifold are examined and an affine connection is given. It is proved that the curvature and torsion of this connection are not tensors. A canonical connection is built. It is shown that the canonical connectionis flat and non-symmetrical.

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Noncommutative Field Theories from a Deformation Point of View

Cited by 2 publications

References 36 publications

Deformation quantization of surjective submersions and principal fibre bundles

Deformation quantization of surjective submersions and principal fibre bundles

On a connection with a torsion non-tensor and a curvature non-tensor

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