Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds

Abstract

After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter $\hslash$, in the case of symplectic manifolds. The graded differential Poisson algebra endows the manifold with a connection, not necessarily torsion-free, and places upon the connection various constraints.

12 pages, no figures. Invited talk at the 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions, 5-10 June 2009, Boston, MA, USA. To appear in the Conference Proceedings