Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds

@article{Derezinski2018PseudodifferentialWC,
title={Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds},
author={J. Derezi'nski and Adam Latosiński and Daniel Siemssen},
journal={Annales Henri Poincar{\'e}},
year={2018},
volume={21},
pages={1595-1635}
}

One can argue that on flat space $${\mathbb {R}}^d$$ R d , the Weyl quantization is the most natural choice and that it has the best properties (e.g., symplectic covariance, real symbols correspond to Hermitian operators). On a generic manifold, there is no distinguished quantization, and a quantization is typically defined chart-wise. Here we introduce a quantization that, we believe, has the best properties for studying natural operators on pseudo-Riemannian manifolds. It is a generalization… CONTINUE READING