论哈密顿衍射的准变形与量子化

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry Pub Date : 2024-06-03 DOI:10.4310/jsg.2023.v21.n5.a1

Laurent,Charles

{"title":"论哈密顿衍射的准变形与量子化","authors":"Laurent,Charles","doi":"10.4310/jsg.2023.v21.n5.a1","DOIUrl":null,"url":null,"abstract":"In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology: the Calabi–Weinstein morphism and a quasimorphism on the universal cover of the Hamiltonian diffeomorphism group introduced by Entov, Py, Shelukhin.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a quasimorphism of Hamiltonian diffeomorphisms and quantization\",\"authors\":\"Laurent,Charles\",\"doi\":\"10.4310/jsg.2023.v21.n5.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology: the Calabi–Weinstein morphism and a quasimorphism on the universal cover of the Hamiltonian diffeomorphism group introduced by Entov, Py, Shelukhin.\",\"PeriodicalId\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-06-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Symplectic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jsg.2023.v21.n5.a1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symplectic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2023.v21.n5.a1","RegionNum":3,"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

摘要

在几何量子化的背景下，我们将任何前量子束自形化与相应量子空间的单元映射联系起来。在半经典极限中，这些映射受控于交映拓扑学的两个不变式：卡拉比-韦恩斯坦变形和恩托夫、派、谢卢欣引入的汉密尔顿衍射群普遍盖上的准变形。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On a quasimorphism of Hamiltonian diffeomorphisms and quantization

In the setting of geometric quantization, we associate to any prequantum bundle automorphism a unitary map of the corresponding quantum space. These maps are controlled in the semiclassical limit by two invariants of symplectic topology: the Calabi–Weinstein morphism and a quasimorphism on the universal cover of the Hamiltonian diffeomorphism group introduced by Entov, Py, Shelukhin.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.