Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-02-20
J.Math.Phys. 44 (2003) 2534-2541
Physics
High Energy Physics
High Energy Physics - Theory
11 pages. Paper shortened. Consideration is now limited to gravity in four-dimensions
Scientific paper
Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to $U(1,1)\times U(1,1).$ No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The four dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.
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