2010/01/31 by Dmitri Vassilevich, D. V. Vassilevich · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/27/9/095020
published as Class.Quant.Grav.27:095020,2010 · 17p; v2: extended version, to appear in CQG
arxiv created 2010/03/12 · openalex publication_date 2010/03/29 · arxiv updated 2010/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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, corresponding 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 corresponds either 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.