Classical and Quantum mechanics on 3D contact manifolds

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2023-11-20 DOI:10.4310/pamq.2023.v19.n4.a5

Yves Colin de Verdière

引用次数: 0

Abstract

In this survey paper, I describe some aspects of the dynamics and the spectral theory of sub-Riemannian 3D contact manifolds. We use Toeplitz quantization of the characteristic cone as 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.

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三维接触流形的经典力学和量子力学

在这篇综述论文中，我描述了亚黎曼三维接触流形的动力学和谱理论的一些方面。我们使用了由Louis Boutet de Monvel和Victor Guillemin引入的特征锥的Toeplitz量化。我们还讨论了我们工作之后的示踪公式以及Duistermaat-Guillemin示踪公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.