The Quantum Mechanical Many-Body Problems and Mathematical Analysis

这一研究致力于量子力学中多体理论的各个方面，场论和微分方程的某些方面，以及纯数学中的一些问题。这些不同的主题是在几十年的研究中发展起来的，其潜在的统一性是，不同问题领域的解决方案相互阐明。主要有四个方面。一是研究金兹堡-朗道涡旋和Skyrmions等模型中的几何对称性破缺。对称破缺问题是现代物理学中的一个关键问题。第二个是关于多体系统中的电子相关性，这是目前超导等领域的中心课题。第三个问题围绕着原子和分子的结构。这些领域的早期工作，特别是矩阵的永久优势问题和函数的斯坦纳对称的连续性或缺乏连续性的问题，是量子力学和分析的有用工具。＊＊＊

9513072 Lieb This research is devoted to various aspects of many- body theory in quantum mechanics, to certain aspects of field theory and differential equations, and to some problems in pure mathematics. These various topics have grown out of a body of research over several decades and the underlying unity is that solutions in the various problem areas shed light on each other. There are four major areas. One is the study of geometric symmetry breaking in such models as Ginzburg- Landau vortices and Skyrmions. The question of symmetry breaking is a crucial one in modern physics. The second concerns electron correlations in many-body systems which, currently, is a central topic in areas such as superconductivity. The third concern centers around the structure of atoms and molecules. The earlier work in these areas, notably the problem of permanent dominance for matrices and the question of the continuity or lack of it for Steiner symmetrization of functions, which is a useful tool in quantum mechanics and analysis. ***