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

国际研究奖学金计划：李群的变形量化和分析

• 批准号: 0202132
• 负责人: Alexander Dvorsky
• 金额: $ 3.19万
• 依托单位: Dvorsky Alexander L
• 依托单位国家: 美国
• 项目类别: Fellowship
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-12-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0202132&HistoricalAwards=false
• 关键词: International; Research; Fellowship; Program; Deformation

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.

0202132德沃斯基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三到二十四个月的研究。 该计划的奖项提供了联合研究的机会，以及使用独特或互补的设施，专业知识和国外的实验条件。该奖项将支持亚历山大L博士为期八个月的研究奖学金。德沃斯基与丹尼尔斯特恩海默博士在法国第戎戎的勃艮第大学合作。该项目的共同资金来自数学和物理科学理事会的多学科活动办公室。量子化是从经典系统开始形成量子力学系统的过程。 存在不同的量化方法，Dvorsky博士对变形量化感兴趣。 直观地说，数学对象的变形是依赖于某个参数的同类对象的族。 一个例子是变形的累积代数的功能（与普通产品）导致非交换的“星产品”适用于量子力学。 该项目致力于变形量子化在李群（对各种经典和量子力学结构的对称性进行编码的数学对象）和李群分析的核心问题上的应用。主持人及其在勃艮第大学的实验室与法国和欧盟其他国家的领先研究有着密切的联系。