{"title":"Classical and Quantum mechanics on 3D contact manifolds","authors":"Yves Colin de Verdière","doi":"10.4310/pamq.2023.v19.n4.a5","DOIUrl":null,"url":null,"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.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2023.v19.n4.a5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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