Tensor calculus on noncommutative spaces

Details Tensor calculus on noncommutative spaces Tensor calculus on noncommutative spaces

2010-01-05

arxiv.org/abs/1001.0766v2

Class.Quant.Grav.27:095020,2010

Physics

High Energy Physics

High Energy Physics - Theory

17p; v2: extended version, to appear in CQG

Scientific paper

10.1088/0264-9381/27/9/095020

It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an infinite number of degrees of freedom per point of the base manifold). We show that on a symplectic manifold this freedom may be almost completely eliminated if one extends the star product to all tensor fields in a covariant way and impose some natural conditions on the tensor algebra. The remaining ambiguity either correspond to constant renormalizations to the symplectic structure, or to maps between classically equivalent field theory actions. We also discuss how one can introduce the Riemannian metric in this approach and the consequences of our results for noncommutative gravity theories.

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