Theoretical Studies of Quantum Systems with Strong Interactions

9509533将对量子场论和凝聚态物理中的非微扰问题进行维格曼理论研究。特别是，具有强相互作用的电子系统和拓扑流体将被研究。要研究的课题包括具有矢量规范相互作用的费米和玻色系统，它们描述了Mott绝缘体、超导体中磁通线的液态、分数量子霍尔效应和拓扑液。研究将集中在规范场的拓扑效应，规范系统的基态特征，拓扑学不稳定性，以及由于量子相变而导致的光谱的分馏。%将调查当前感兴趣的各种物理系统。所有这些系统的特点都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. ***