The Quantum Mechanical Many-Body Problems and Mathematical Analysis

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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. ***