Classical and Quantum mechanics on 3D contact manifolds

TL;DR

This survey explores the dynamics and spectral theory of 3D contact manifolds using Toeplitz quantization, trace formulae, and their applications in classical and quantum mechanics.

Contribution

It introduces the application of Toeplitz quantization to 3D contact manifolds and discusses trace formulae in this context, advancing understanding of their spectral properties.

Findings

Application of Toeplitz quantization to contact manifolds

Derivation of trace formulae for spectral analysis

Insights into classical and quantum dynamics on contact manifolds

Abstract

In this survey paper, I describe some aspects of the dynamics and the spectral theory of sub-Riemannian3D contact manifolds. We use Toeplitz quantization of the characteristic coneas introduced by Louis Boutet de Monvel and Victor Guillemin. We also discuss trace formulae following our work as well as the Duistermaat-Guillemin trace formula.