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

在一般理论领域， 基本粒子物理学，将集中在各个方面， 二维量子场论，这是重要的， 数学问题的解决，出现在 理解超弦理论和统计系统。 （超级）弦理论，被认为提供了基本的 理解自然界的基本力量， 基本的数学和量子力学描述， 二维量子场论的形式和方法。 同样的形式主义和方法被用于研究 某些一维和二维统计力学模型 它描述了不同系统的行为，例如长- 链分子和膜，并可能解释某些 如高温超导现象。 无论是 在某些情况下，显然可以取得很大进展， 在处理“可积”的情况下 系统，因为在这种情况下， 可以得到相应的数学问题。 是 我相信，相关的可积系统可以被描述为 以两种互补但等同的方式，要么如此- 称为刘维和户田理论，或作为非局部诱导 引力和W引力理论 研究将集中在 这些理论的研究，并预计将提供 关于字符串的重要信息和解释 自然的基本力量，以及信息 在许多实际应用中， 应用.

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.