{"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":"17 1","pages":""},"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}
引用次数: 0
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.
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.