Mathematical Sciences: Research on Conformal Field Theory

数学科学：共形场论研究

• 批准号: 9400841
• 负责人: Giovanni Felder
• 金额: $ 9.67万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-05-01 至 1997-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400841&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Conformal; Field

940841 Felder The main goal of the proposed activity is to give an explicit description of conformal blocks on Riemann surfaces, as a space of solutions of a system of differential equations, generalizing the Knizhnik-Zamolodchikov equations. Properties of the equations and their solutions will be investigated. In particular, integral representations of the solutions will be calculated, with applications to the topology of configuration spaces on surfaces, invariants of three-dimensional manifolds, and the theory of quantum groups and integrable systems. Conformal Field Theory finds its origin in the physics of surface at critical temperature, and string theory, a unified model of particle interactions. The object of this research is the mathematical structure of Conformal Field Theory. This theory explicitly associates a mathematical object called a complex vector space of "conformal blocks" with equations that model physical systems. ***

小行星940841 拟议活动的主要目标是给出黎曼曲面上的共形块的明确描述，作为微分方程系统的解的空间，推广Knizhnik-Zamolodchikov方程。将研究方程及其解的性质。特别是，积分表示的解决方案将计算，与应用程序的拓扑结构的配置空间的表面，不变量的三维流形，量子群和可积系统的理论。 共形场论起源于临界温度下的表面物理学，以及粒子相互作用的统一模型弦理论。本文的研究对象是共形场论的数学结构。该理论明确地将一个称为“共形块”的复向量空间的数学对象与模拟物理系统的方程相关联。 ***