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arXiv · hep-th/0007181

Noncommutative Quantum Gravity

J. W. Moffat
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Abstract

The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a complex Hermitian, nonsymmetric $g_{μν}$ and discuss the problems associated with such a theory. We then introduce a complex symmetric (non-Hermitian) metric, with the associated complex connection and curvature, as the basis of a noncommutative spacetime geometry. The spacetime coordinates are in general complex and the group of local gauge transformations is associated with the complex group of Lorentz transformations CSO(3,1). A real action is chosen to obtain a consistent set of field equations. A Weyl quantization of the metric associated with the algebra of noncommuting coordinates is employed.

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J. W. Moffat. 2000-09-25. Noncommutative Quantum Gravity. https://doi.org/10.1016/s0370-2693(00)01064-9

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