Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 282

A deformation theoretical approach to Weyl quantization on Riemannian manifolds

M. J. Pflaum.

By using a sheaf theoretical language we introduce a notion of deformation quantization allowing not only for formal deformation parameters but for real or complex ones as well. As a model for this approach to deformation quantization we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Hereby we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star-products on a cotangent bundle.

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