Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle. (English) Zbl 1368.83050
Summary: A model of noncommutative gravity is constructed by means of B. Fedosov [Deformation quantization and index theory. Berlin: Akademie Verlag (1996; Zbl 0867.58061)] deformation quantization of an endomorphism bundle. The fields describing noncommutativity – symplectic form and symplectic connection – are dynamical, and the resulting theory is coordinate covariant and background independent. Its interpretation in terms of a Seiberg-Witten map is provided. Also, a new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.
MSC:
83C65 | Methods of noncommutative geometry in general relativity |
83C45 | Quantization of the gravitational field |
58J22 | Exotic index theories on manifolds |
53D55 | Deformation quantization, star products |