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

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。该计划的奖励为联合研究提供了机会，并利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Alexander L. Dvorsky博士与Daniel Sternheimer博士在法国第戎的Bourgogne大学进行为期八个月的研究。该项目的共同资助来自数学和物理科学理事会的多学科活动办公室。量子化是由经典量子力学系统开始形成量子力学系统的过程。存在不同的量子化方法，德沃斯基博士对变形量子化感兴趣。直观地说，数学对象的变形是依赖于某些参数的同类对象的一组。一个例子是变形函数的交换代数（与普通积）导致适合量子力学的非交换“星积”。该项目解决了变形量子化在李群（编码各种经典和量子力学结构对称性的数学对象）和李超群分析的核心问题中的应用。主持人和他在勃艮第大学的实验室与法国和欧盟其他国家的主要研究有着密切的联系。

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.