Computer Science
Scientific paper
Jan 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cqgra..24...15z&link_type=abstract
Classical and Quantum Gravity, Volume 24, Issue 1, pp. 15-26 (2007).
Computer Science
6
Scientific paper
We study the problem of reality in the geometric formalism of the 4D noncommutative gravity using the known deformation of the diffeomorphism group induced by the twist operator with the constant deformation parameters ϑmn. It is shown that the real covariant derivatives can be constructed via sstarf-anticommutators of the real connection with the corresponding fields. The minimal noncommutative generalization of the real Riemann tensor contains only ϑmn-corrections of the even degrees in comparison with the undeformed tensor. The gauge field hmn describes a gravitational field on the flat background. All geometric objects are constructed as the perturbation series using sstarf-polynomial decomposition in terms of hmn. We consider the nonminimal tensor and scalar functions of hmn of the odd degrees in ϑmn and remark that these pure noncommutative objects can be used in the noncommutative gravity.
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