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}
}
  • J. Derezi'nski, Adam Latosiński, Daniel Siemssen
  • Published 2018
  • Mathematics, Physics
  • Annales Henri Poincaré
  • 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
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