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 $\hbar$, 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.
Categories: hep-th