Matteo A Cardella and Daniela Zanon 2003 Class. Quantum Grav. 20 L95 doi:10.1088/0264-9381/20/8/101
Matteo A Cardella and Daniela Zanon
Show affiliationsWe construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein–Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints ensure that it is not topological. We find that the choice of the gauge group and of the constraints is crucial in recovering a correct deformation of standard gravity. Using the Seiberg–Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve the constraints explicitly and exhibit the first-order noncommutative corrections to the Einstein–Hilbert action.
53D55 Deformation quantization, star products
81T75 Noncommutative geometry methods (See also 46L85, 46L87, 58B34)
83C65 Methods of noncommutative geometry (See also 58B34)
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
Issue 8 (21 April 2003)
Received 17 January 2003, in final form 25 February 2003
Published 20 March 2003
Matteo A Cardella and Daniela Zanon 2003 Class. Quantum Grav. 20 L95
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