Theoretical Studies of Quantum Systems with Strong Interactions

9509533 Wiegmann理论研究将在量子场论和凝聚态物理学的非微扰问题进行。 特别是，将研究具有强相互作用和拓扑流体的电子系统。 将研究的主题包括费米和玻色系统与矢量规范相互作用，描述莫特绝缘体，超导体中的磁通线，分数量子霍尔效应和拓扑液体的液体状态。 研究将集中在规范场的拓扑效应，规范系统的基态的特性，拓扑不稳定性，以及作为量子相变的结果的光谱的分形。 将研究当前感兴趣的各种物理系统。 所有这些系统的特点是，它们是强相互作用的，不能用现有的理论技术来处理。 理论方法将是一种使用场论技术的数学方法。 这项工作的结果将有助于凝聚态物理及其数学基础。 ***

9509533 Wiegmann Theoretical research will be conducted on nonperturbative problems in quantum field theory and condensed matter physics. In particular, electronic systems with strong interactions and topological fluids will be studied. Topics to be studied include Fermi and Bose systems with vector gauge interactions which describe the Mott insulator, liquid state of flux lines in superconductors, fractional quantum Hall effect, and topological liquids. The research will focus on topological effects of the gauge field, the character of the ground state of the gauged system, toplogical instability, and fractionalization of the spectrum as a result of a quantum phase transition. %%% A variety of physical systems will be investigated which are of current interest. All of these systems are characterized by the fact that they are strongly interacting and cannot be treated using existing theoretical techniques. The theoretical approach will be a mathematical one using field theoretical techniques. The results of this work will contribute to both condensed matter physics and its mathematical foundations. ***