通过扭转的哈密顿作用的量子化

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry Pub Date : 2018-04-17 DOI:10.4310/JSG.2020.V18.N2.A2

P. Bieliavsky, C. Esposito, R. Nest

{"title":"通过扭转的哈密顿作用的量子化","authors":"P. Bieliavsky, C. Esposito, R. Nest","doi":"10.4310/JSG.2020.V18.N2.A2","DOIUrl":null,"url":null,"abstract":"In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfel'd twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle stucture and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfel'd approach.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"14 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2018-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantization of Hamiltonian coactions via twist\",\"authors\":\"P. Bieliavsky, C. Esposito, R. Nest\",\"doi\":\"10.4310/JSG.2020.V18.N2.A2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfel'd twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle stucture and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfel'd approach.\",\"PeriodicalId\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-04-17\",\"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.2020.V18.N2.A2\",\"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.2020.V18.N2.A2","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

本文引入了具有Drinfel扭曲结构的Hopf代数的量子哈密顿(co)作用的概念。2-cocycles)。首先，我们定义了与2环结构相容的泊松李群的经典哈密顿作用，并讨论了一个具体的例子。这允许我们在经典动量图的基础上，构造一个Hopf协同作用下的量子动量图，并使用德林费尔方法将其量子化。

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

Quantization of Hamiltonian coactions via twist

In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfel'd twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle stucture and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfel'd approach.

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.