Symplectic microgeometry, IV: Quantization
| Autor: | Benoit Dherin, Alberto S. Cattaneo, Alan Weinstein |
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| Přispěvatelé: | University of Zurich, Cattaneo, Alberto S |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
General Mathematics 340 Law Semiclassical physics 610 Medicine & health 01 natural sciences Fourier integral operator Schrödinger equation Quantization (physics) symbols.namesake 510 Mathematics Operator (computer programming) Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Trigonometric functions 0101 mathematics Mathematics::Symplectic Geometry 2600 General Mathematics Mathematics Functor 010102 general mathematics 10123 Institute of Mathematics Mathematics - Symplectic Geometry symbols Symplectic Geometry (math.SG) 010307 mathematical physics Symplectic geometry |
| Zdroj: | Pacific Journal of Mathematics. 312:355-399 |
| ISSN: | 1945-5844 0030-8730 |
| DOI: | 10.2140/pjm.2021.312.355 |
| Popis: | 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. Comment: 47 pages |
| Databáze: | OpenAIRE |
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