Symplectic microgeometry, IV: Quantization

@article{Cattaneo2021SymplecticMI,
  title={Symplectic microgeometry, IV: Quantization},
  author={Alberto S. Cattaneo and Benoit Richard Umbert Dherin and Alan D. Weinstein},
  journal={Pacific Journal of Mathematics},
  year={2021}
}
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the cotangent microbundle category, and they admit a total symbol calculus in terms of symplectic micromorphisms enhanced with half-density germs. This new operator category encompasses the semi-classical pseudo-differential calculus and offers a functorial… 
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This paper contains three results about generating functions for Lie-theoretic integration of Poisson brackets and their relation to quantization. In the first, we show how to construct a generating

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