Algebraic structures in quantum field theories

我的研究兴趣的中心主题是关于自然的对称性以及这些对称性之间的关系。更具体地说，我研究运动代数，如Poincaré代数(构成所有相对论理论的基础)、伽利莱代数(牛顿物理学的基本原理)、德西特(具有相对论弯曲时空)、牛顿-胡克(非相对论弯曲时空)等。连接这些对称性的数学过程称为李代数的“收缩”和“变形”。原则上，它们允许人们从相关的对称性中推断出关于某些对称性的进一步知识。我将把这些技术应用于其他类型的对称性，如无穷维李代数，它出现在共形场论中，如弦理论或统计物理的临界现象。

The central topic of my research interests revolves about the symmetries of Nature and the relations between these symmetries. More specifically, I study kinematical algebras such as Poincaré algebra (which underlies all relativistic theories), Galilei algebra (fundamental in Newtonian physics), de Sitter (with relativistic curved space-time), Newton-Hooke (non-relativistic curved space-time), etc. The mathematical procedures which connect these symmetries are called "contractions" and "deformations" of Lie algebras. In principle, they allow one to deduce further knowledge about some symmetries from the associated symmetries. I will apply these techniques to other types of symmetries such as the infinite-dimensional Lie algebras which occur in conformal field theories such as string theory or the critical phenomena of statistical physics.