Semiclassical states associated to isotropic submanifolds of phase space

TL;DR

This paper introduces new classes of quantum states linked to isotropic submanifolds in phase space, with a developed semiclassical calculus and stability properties, applicable in various quantum analysis contexts.

Contribution

It defines and analyzes semiclassical states associated to isotropic submanifolds, including their stability under operators and a novel symbol calculus involving symplectic spinors.

Findings

States are stable under semiclassical pseudo-differential operators.

States are covariant under semiclassical Fourier integral operators.

A semiclassical symbol calculus with symplectic spinors is developed.

Abstract

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.