Vol. 312, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 328: 1
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Symplectic microgeometry, IV: Quantization

Alberto S. Cattaneo, Benoit Dherin and Alan Weinstein

Vol. 312 (2021), No. 2, 355–399

We construct a special class of semiclassical Fourier integral operators whose wave fronts are the symplectic micromorphisms of our previous work (J. Symplectic Geom. 8 (2010), 205–223). 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 semiclassical pseudodifferential calculus and offers a functorial framework for the semiclassical analysis of the Schrödinger 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.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

quantization, Fourier integral operators, symplectic micromorphisms
Mathematical Subject Classification
Primary: 58J40, 81S10
Received: 3 August 2020
Revised: 30 January 2021
Accepted: 1 May 2021
Published: 31 August 2021
Alberto S. Cattaneo
Universität Zürich
Benoit Dherin
Google, Inc.
Alan Weinstein
University of California
Berkeley, CA
United States