{"title":"Berezin-Toeplitz量化表示的几何构造","authors":"Kwokwai Chan, N. Leung, Qin Li","doi":"10.4310/ATMP.2022.v26.n1.a1","DOIUrl":null,"url":null,"abstract":"For a K\\\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\\infty(X)[[\\hbar]],\\star_{BT})$ parametrized by points $z_0 \\in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}\\left( X,L^{\\otimes m}\\right) $ around $z_{0}$.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":"284 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"A geometric construction of representations of the Berezin–Toeplitz quantization\",\"authors\":\"Kwokwai Chan, N. Leung, Qin Li\",\"doi\":\"10.4310/ATMP.2022.v26.n1.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a K\\\\\\\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\\\\infty(X)[[\\\\hbar]],\\\\star_{BT})$ parametrized by points $z_0 \\\\in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}\\\\left( X,L^{\\\\otimes m}\\\\right) $ around $z_{0}$.\",\"PeriodicalId\":50848,\"journal\":{\"name\":\"Advances in Theoretical and Mathematical Physics\",\"volume\":\"284 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2020-01-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.4310/ATMP.2022.v26.n1.a1\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/ATMP.2022.v26.n1.a1","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
A geometric construction of representations of the Berezin–Toeplitz quantization
For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$ parametrized by points $z_0 \in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}\left( X,L^{\otimes m}\right) $ around $z_{0}$.
期刊介绍:
Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.