Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor calculus on noncommutative spaces   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.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom