Mathematical Sciences: Integrable Models in Mathematics and Physics

数学科学：数学和物理中的可积模型

• 批准号: 9001794
• 负责人: Craig Tracy
• 金额: $ 12.45万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001794&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integrable; Models; Mathematics

This research involves the quantum field theory of fermions on the Poincare disk and the hard hexagon model - a lattice gas model in statistical mechanics. The research on the quantum theory of fermions will involve expressing the Schwinger functions in terms of certain nonlinear deformation equations. These equations will then be analyzed both in the Euclidean limit and in the conformal field theory limit. An important aspect of this work is the extension of the existing theory to the noneuclidean setting which may lay the groundwork for extensions to Riemann surfaces of a more general type. The research on the hard hexagon model will involve derivations of differential equations for the partition function and density functions. An attempt will be made to extend these equations to the hard square lattice gas, a model that is 'not solvable' by present techniques. This research is in the general area of theoretical physics and deals with isomonodromy deformations and applications to conformal field theory, statistical mechanics, and scattering theory.

这项研究涉及庞加莱盘上费米子的量子场论和硬六边形模型——统计力学中的晶格气体模型。 费米子量子理论的研究将涉及用某些非线性变形方程来表达施温格函数。 然后将在欧几里得极限和共形场论极限下分析这些方程。 这项工作的一个重要方面是将现有理论扩展到非欧几里德设置，这可能为扩展到更一般类型的黎曼曲面奠定基础。 硬六边形模型的研究将涉及配分函数和密度函数微分方程的推导。 我们将尝试将这些方程扩展到硬方晶格气体，这是现有技术“无法求解”的模型。 这项研究属于理论物理的一般领域，涉及等单性变形及其在共形场理论、统计力学和散射理论中的应用。