Algebraic Structures and Correlations in Quantum Many-Body Systems

量子化超代数等代数结构是数学中最重要的发现之一，在物理学中有广泛的应用。最近国际上对顶点算子和这些代数结构的表示及其在可积系统和量子场论中的应用感到兴奋。我为这个迅速发展的领域做出了重大贡献，并将利用这一成功。我将发展一个全面的理论，这些数学结构和它们的应用，在建设相关函数和形状因素，并在这样做写一个明确的专题论文。

Algebraic structures such as quantized superalgebras are among the most important discoveries in mathematics and have applications in a wide range of physics. Internationally there has been recent excitement about vertex operators and representations of these algebraic structures and their applications to integrable systems and quantum field theory. I have made significant contributions to this rapidly expanding field, and will capitalize on this success. I will develop a comprehensive theory of these mathematical structures and their applications in the construction of correlation functions and form factors, and in so doing write a definitive monograph on the subject.