DEFORMATION QUANTIZATION ON COTANGENT BUNDLES

In this note we construct natural star-products on cotangent bundles of Riemannian manifolds. Hereby we essentially use a parameter dependent symbol calculus for pseudodifferential operators on manifolds. The constructed star-products generalize the well-known (lambdal)-ordered quantization scheme on R^2n. In particular we thus extend Weyl quantization but also normal and antinormal order quantization to cotangent bundles of Riemannian manifolds.