Mathematical Sciences: Statistical Mechanics and Quantum Field Theory

数学科学：统计力学和量子场论

• 批准号: 8802590
• 负责人: Hans Koch
• 金额: $ 5.81万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802590&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Mechanics; Quantum

This project in mathematical physics has to do with the rigorous analysis of renormalization group techniques used in a heuristic fashion by physicists. ( The basic physical problem is to determine macroscopic properties of large systems of particles with known short range interactions. ) Some of the work involves a novel use of the computer to assist in finding proofs of theorems that require intricate schemes for estimating quantities. Renormalization group techniques have proved to be a powerful tool in statistical mechanics, especially in the theory of critical phenomena. The same techniques also play a dominant role in the modern approach to constructive quantum field theory. Much of the current research in these two areas is concerned with the extension of present methods from relatively simple to more realistic systems. Professor Koch will continue his investigation of models relevant to the theory of critical phenomena. His second main emphasis is an analysis of disordered systems such as the Hopfield model and the Sherrington - Kirkpatrick model, which exhibit spin glass behavior for a certain range of parameters.

数学物理学中的这个项目与物理学家以启发式方式使用的重整化群技术的严格分析有关。 （基本的物理问题是确定具有已知短程相互作用的大型粒子系统的宏观性质。）其中一些工作涉及计算机的新颖用途，以协助寻找需要复杂方案来估计数量的定理证明。 重正化群技术已被证明是统计力学中的强大工具，特别是在临界现象理论中。 同样的技术也在现代构造性量子场论方法中发挥着主导作用。 当前这两个领域的大部分研究都涉及将现有方法从相对简单的系统扩展到更现实的系统。 科赫教授将继续研究与临界现象理论相关的模型。 他的第二个主要重点是对无序系统的分析，例如 Hopfield 模型和 Sherrington - Kirkpatrick 模型，这些模型在一定参数范围内表现出自旋玻璃行为。