Mathematical Sciences: Statistical Mechanics and Quantum Field Theory

数学科学：统计力学和量子场论

• 批准号: 9103590
• 负责人: Hans Koch
• 金额: $ 6.94万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103590&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Mechanics; Quantum

Professor Koch will continue his investigations of models relevant to the theory of critical phenomena, and of neural network models related to disordered systems in statistical mechanics. This includes the development of new techniques in renormalization group analysis, which connects his work to constructive quantum field theory, where similar methods are being used. Professor Koch's work is in the area broadly known as mathematical physics where a deep mathematical understanding of physical models is sought. One of his projects involves an investigation of the renormalization group, where an attempt is made to understand interactions at all length scales simultaneously. This is one of the most important and least understood problems in statistical mechanics and quantum field theory today.

科赫教授将继续研究与临界现象理论相关的模型，以及与统计力学中无序系统相关的神经网络模型。 这包括重正化群分析新技术的开发，这将他的工作与建设性量子场论联系起来，其中也使用了类似的方法。 科赫教授的工作属于众所周知的数学物理学领域，寻求对物理模型的深刻数学理解。 他的一个项目涉及对重正化群的研究，试图同时理解所有长度尺度的相互作用。 这是当今统计力学和量子场论中最重要和最难理解的问题之一。