Quantum Field Theory: Two-Dimensional Integrable Systems, Exact S-Matrices, and Nonlocal Field Theories

量子场论：二维可积系统、精确 S 矩阵和非局部场论

• 批准号: 9222318
• 负责人: Marcus Grisaru
• 金额: $ 20.13万
• 依托单位: Brandeis 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: 1993-03-15 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9222318&HistoricalAwards=false
• 关键词: Quantum; Field; Theory; Two; Dimensional

The research, in the general area of theoretical elementary particle physics, will concentrate on aspects of two-dimensional quantum field theory which are important in the solution of mathematical problems that arise in the understanding of superstring theory and statistical systems. (Super)string theory, which is believed to provide the basic understanding of the fundamental forces of nature, has as its underlying mathematical and quantum-mechanical description the formalism and methods of two-dimensional quantum field theory. The same formalism and methods are used in the study of certain one- and two-dimensional statistical mechanics models which describe the behavior of diverse systems such as long- chain molecules and membranes, and may explain certain phenomena such as high temperature superconductivity. In both cases it has become apparent that much progress can be made in those situations where one is dealing with "integrable" systems, because in such situations a complete solution of the corresponding mathematical problems can be obtained. It is believe that the relevant integrable systems can be described in two complementary, but equivalent, manners, either as so- called Liouville and Toda theories, or as nonlocal induced gravity and W-gravity theories. The research will focus on the study of such theories and is expected to provide important information concerning strings and the explanation of the fundamental forces of nature, as well as information about statistical systems which arise in many practical applications.

在理论基本粒子物理的一般领域，研究将集中在二维量子场论的各个方面，这对于解决在理解超弦理论和统计系统时出现的数学问题很重要。（超）弦理论被认为提供了对自然界基本力的基本理解，它的基础数学和量子力学描述是二维量子场论的形式主义和方法。同样的形式和方法被用于研究某些一维和二维统计力学模型，这些模型描述了不同系统的行为，如长链分子和膜，并可以解释某些现象，如高温超导。在这两种情况下，很明显，在处理“可积”系统的情况下，可以取得很大的进展，因为在这种情况下，可以获得相应数学问题的完全解。相信相关的可积系统可以用两种互补但等效的方式来描述，即所谓的Liouville和Toda理论，或非局部诱导引力和w -引力理论。这项研究将集中在这些理论的研究上，预计将提供关于弦的重要信息和对自然基本力的解释，以及在许多实际应用中出现的统计系统的信息。