# 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…

## 2 Citations

On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms

- Mathematics
- 2020

Generating Functions for Local Symplectic Groupoids and Non-perturbative Semiclassical Quantization

- MathematicsCommunications in Mathematical Physics
- 2022

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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