A deformation-theoretical approach to Weyl quantization on Riemannian manifolds. (English) Zbl 0995.53057

Pflaum, Markus J.

Lett. Math. Phys. 45, No. 4, 277-294 (1998).

Summary: By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also 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. Here, 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.

MSC:

53D55

Deformation quantization, star products

Keywords:

deformation quantization; cotangent bundles; symbol calculus; pseudodifferential operators; star products