Infinite Dimensional Lie Algebras, Quantum Groups and their Applications

无限维李代数、量子群及其应用

• 批准号: 0901431
• 负责人: Nicolai Reshetikhin
• 金额: $ 32.69万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901431&HistoricalAwards=false
• 关键词: Infinite; Dimensional; Lie; Algebras; Quantum

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The proposal is focused on problems which lie at the interface of representation theory and mathematical physics. More specially, it aims at problems in the representation theory of quantum groups at roots of 1, on invariants of 3-manifolds, certain problems in local quantum field theory (such as the construction of perturbative Chern-Simons theory), and on problems in integrable systems and solvable models of statistical mechanics.One of the central questions in modern theoretical physics is the construction of the model of fundamental interaction which is consistent with the experiment and mathematically adequate. The framework of local quantum field theory is main concept behind the standard model. However the framework of quantum field theory still largely remain a mathematical puzzle. Part of my research will focus on understanding this puzzle in the context of semi-classical quantization. The goal of other parts of the proposal is the construction of topological and integrable quantum field theories combinatorically and the study of emerging algebraic and analytical problems.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该提案的重点是位于表征理论和数学物理界面的问题。更具体地说，它针对的问题，在表示理论的量子群在根1，不变量的3流形，某些问题，在当地的量子场论（如微扰陈-西蒙斯理论的构建），现代理论物理学的中心问题之一是基本相互作用模型的构造，与实验结果一致，数学上也是足够的。局域量子场论的框架是标准模型背后的主要概念。然而，量子场论的框架在很大程度上仍然是一个数学难题。我的部分研究将集中在半经典量子化的背景下理解这个难题。该提案的其他部分的目标是拓扑和可积量子场论组合的建设和新兴的代数和分析问题的研究。