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arXiv · 2007.08167

Symplectic Microgeometry IV: Quantization

Alberto S. Cattaneo·Benoit Dherin·Alan Weinstein
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Abstract

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 framework for the semi-classical analysis of the Schr\"odinger equation. We also comment on applications to classical and quantum mechanics as well as to a functorial and geometrical approach to the quantization of Poisson manifolds.

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Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein. 2020-07-16. Symplectic Microgeometry IV: Quantization. https://doi.org/10.2140/pjm.2021.312.355

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