Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-07-23
Phys.Lett. B491 (2000) 345-352
Physics
High Energy Physics
High Energy Physics - Theory
13 pages LaTex. Changes to text and new text added. To be published in Physics Letters B
Scientific paper
10.1016/S0370-2693(00)01064-9
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 $g_{\mu\nu}$ 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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