The Quantum Mechanical Many-Body Problems and Mathematical Analysis

小行星9513072 这项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。 这些不同的主题已经从几十年来的研究中发展出来，潜在的统一性是各个问题领域的解决方案相互启发。 有四个主要领域。 一个是对Ginzburg-朗道涡旋和Skyrmions等模型中几何对称破缺的研究。 对称性破缺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。 第三个关注点是原子和分子的结构。 早期的工作在这些领域，特别是问题的永久优势的矩阵和问题的连续性或缺乏它的施泰纳对称化的职能，这是一个有用的工具，在量子力学和分析。 ***

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. ***