Semiclassical states associated to isotropic submanifolds of phase space

Victor Guillemin, Alejandro Uribe, Zuoqin Wang

Published 2015-11-04Version 1

We define classes of quantum states associated to isotropic submanifolds of cotangent bundles. The classes are stable under the action of semiclassical pseudo-differential operators and covariant under the action of semiclassical Fourier integral operators. We develop a semiclassical symbol calculus for them; the symbols are symplectic spinors. We outline various applications.