Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle

Abstract

Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -- symplectic form and symplectic connection -- are dynamical, and the resulting theory is completely coordinate covariant and background independent. Its interpretation in terms of Seiberg-Witten map is provided. Also, new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.

22 pages, section 3.2 reworked, various minor corrections. (This is an author-created, un-copyedited version of an article accepted for publication in Clasical and Quantum Gravity)

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Cited by in corpus (7)

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• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• Field Theory with Coordinate Dependent Noncommutativity