Tensor calculus on noncommutative spaces
arXiv:1001.0766 · doi:10.1088/0264-9381/27/9/095020
Abstract
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.
17p; v2: extended version, to appear in CQG
References in corpus (16)
- A Gravity Theory on Noncommutative Spaces
- Symmetry, Gravity and Noncommutativity
- Twisted Gauge Theories
- Noncommutative Gravity Solutions
- Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
- Twist to close
- Star products made (somewhat) easier
- Drinfeld Twist and General Relativity with Fuzzy Spaces
- Exact Black Hole Solutions in Noncommutative Gravity
- Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds
- Diffeomorphism covariant star products and noncommutative gravity
- Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
- Universal star products
- Gauge Theory of the Star Product
- Gauge field theories with covariant star-product
- Noncommutative Solitons of Gravity
Cited by in corpus (7)
- On some models of geometric noncommutative general relativity
- Field Theory on Curved Noncommutative Spacetimes
- Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
- SL(2,C) gravity on noncommutative space with Poisson structure
- Non-commutative Kerr black hole
- U(2,2) gravity on noncommutative space with symplectic structure
- Field Theory with Coordinate Dependent Noncommutativity