New approaches and applications of integrable quantum field theory

该项目旨在为可积系统理论开发新的数学方法，以获得二维量子场论的各种非线性模型的精确解。该项目是基于经典和量子系统之间的一个意想不到的对应关系，它为描述可积量子场论的物理有趣模型提供了一个强大的方法。预期成果包括非线性sigma模型的精确解，这些模型在许多领域都有重要应用，包括凝聚态物理学、弦理论和场论以及黎曼几何。该项目预计将为物理和数学知识的进步提供重大利益。

This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact solutions to non-linear sigma-models which have important applications in many areas, including condensed matter physics, string and field theories and Riemannian geometry. The project expects to provide significant benefit to the advancement of knowledge in physics and mathematics.