International Research Fellowship Program: Deformation Quantization and Analysis on Lie Groups

0202132Dvorky国际研究奖学金计划使美国科学家和工程师能够在国外进行3至24个月的研究。该计划的奖项提供了联合研究的机会，并利用国外独特或互补的设施、专业知识和实验条件。该奖项将支持亚历山大·L·德沃斯基博士与法国第戎勃艮第大学的丹尼尔·斯特恩海默博士合作的为期8个月的研究奖学金。这个项目的共同资金来自数学和物理科学委员会的多学科活动办公室。量子化是从经典量子力学系统开始形成的过程。有不同的量化方法，德沃斯基博士对形变量化很感兴趣。直观地说，数学对象的变形是依赖于某个参数的一族同类对象。一个例子是，用普通积对变函数代数，得到适用于量子力学的非对易“星积”。这个项目致力于将形变量子化应用于李群(编码各种经典和量子力学结构的对称性的数学对象)和李超群分析的中心问题。东道主和他在勃艮第大学的实验室与法国和其他欧盟国家进行的领先研究有很强的联系。

0202132DvorskyThe International Research Fellowship Program enables U.S. scientists and engineers to conduct three to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support an eight month research fellowship by Dr. Alexander L. Dvorsky to work with Dr. Daniel Sternheimer at the University de Bourgogne in Dijon, France. Co-funding for this project comes from the Math and Physical Science Directorate's Office of Multidisciplinary Activities.Quantization is the process of forming a quantum-mechanical system starting from a classical one. There exist different methods of quantization, and Dr. Dvorsky is interested in deformation quantization. Intuitively a deformation of a mathematical object is a family of the same kind of objects depending on some parameter. An example is deforming a cummutative algebra of functions (with the ordinary product) leads to the non-commutative "star-products" suitable for quantum mechanics. This project addresses the applications of deformation quantization to the central questions of analysis on Lie groups (mathematical objects which encode the symmetries of various classical-and quantum-mechanical constructions) and Lie supergroups.The host and his laboratory at the Universite de Bourgogne have strong connections with leading research performed in France and other countries of the European Union.