Mathematical Sciences: Group Representations & Conformal Field Theory

扎克曼教授将研究非紧致李群作为手征模型的内部对称群在物理学中的作用。Minkowski时空的洛伦兹群是Zuckerman理论中的一个基本例子。因此，几何对称性和内部对称性之间的区别在这项工作中变得有些模糊。这种模糊可能与手征模型和非紧致群在二维和三维量子引力中的应用有关。几乎从物理学的这些分支开始，对称性原理就在量子力学和量子场论中扮演着重要的角色。量子系统可能具有几何对称性--继承自背景时空连续体--和/或内部对称性--与额外的自由度相关。扎克曼教授将研究这些对称性的基本数学。

Professor Zuckerman will investigate the role of noncompact Lie groups as internal symmetry groups of chiral models in physics. The Lorentz group of Minkowski space-time is a basic example in Zuckerman's theory. Thus the distinction between geometrical and internal symmetries becomes somewhat blurred in this work. This blurring may be relevant to applications of chiral models and noncompact groups to quantum gravity in two and three dimensions. Symmetry principles have played an essential role in quantum mechanics and quantum field theory almost from the inception of these branches of physics. A quantum system may have geometrical symmetries - inherited from the background space-time continuum - and or internal symmetries - related to additional degrees of freedom. Professor Zuckerman will investigate the basic mathematics of these symmetries.