Mathematical Sciences: Group Representations & Conformal Field Theory

Zuckerman教授将研究非紧的作用 李群作为手征模型的内对称群 物理学 闵可夫斯基时空的洛伦兹群是一个基本的 Zuckerman理论中的一个例子。 因此， 几何和内部对称性变得有些模糊， 这项工作 这种模糊可能与 手征模型和非紧群的量子引力在两个和 三维空间 对称性原理在量子力学中起着重要作用 力学和量子场论几乎从一开始 物理学的这些分支。 量子系统可以具有几何 从背景时空连续体继承而来的对称性 和/或内部对称性-与附加的 自由 朱克曼教授将研究 这些对称性的数学。

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.