Mathematical Sciences: Problems in Conformal Field Theory

数学科学：共形场论问题

• 批准号: 9307086
• 负责人: Gregg Zuckerman
• 金额: $ 24.25万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307086&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Conformal; Field

Zuckerman will investigate topological conformal field theory. He will study the algebraic structures that are naturally defined in the state space of a TCFT. He will also investigate TCFT as a broad class of models that include the conformal string backgrounds. Khesin will continue to investigate the role of the Virasoro Lie algebra and Lie group in one dimensional fluid dynamics and two dimensional nonlinear wave propagation. He will also pursue his study of higher analogs of the Poisson bracket algebra associated to the Virasoro Lie algebra. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.

祖克曼将研究拓扑共形场论。 他将研究 TCFT 状态空间中自然定义的代数结构。 他还将研究 TCFT 作为包括共形弦背景的广泛模型。 Khesin 将继续研究 Virasoro 李代数和李群在一维流体动力学和二维非线性波传播中的作用。 他还将继续研究与 Virasoro Lie 代数相关的泊松括号代数的高级类似物。 现代物理学、量子力学和相对论，是二十世纪的产物。 它牢固地建立在上个世纪解决物质微观结构并掌握远距离作用、电磁和热辐射概念的尝试中。 这些发展的数学基础统称为数学物理，范围从控制粒子动力学的薛定谔算子的详细分析，到试图将四种已知力统一为一个理论的统一场论。