Mathematical Sciences: Spectral and Variational Problems of Mathematical Physics

这个数学研究项目将对起源于理论物理的几个主题进行光谱分析和变分分析。它既是纯粹的数学，也是应用数学：它的目的之一是推导物理学家可以实际使用的公式，而纯粹的意义是它包括证明严格的定理。物理重要性的量通常是某些泛函或线性算子的特征值和特征向量的最小化。在这项研究中，它们大多起源于量子物理，如单个粒子或块状物质的薛定谔算符，或重子的Skyrme模型。主要研究人员将通过将抽象技术(主要来自泛函分析)与更具体的工具(例如微分方程式理论或微扰技术)相结合，继续他们在这些主题和其他主题上的工作。来自物理和数值计算的直觉预计也会有所帮助。

This mathematical research project will undertake spectral and variational analysis of several topics originating in theoretical physics. It is both pure and applied mathematics: applied in the sense that one of the goals is the derivation of formulae that a physicist can actually use, and pure in that it consists of proving rigorous theorems. Quantities of physical importance are frequently minimizers of certain functionals or eigenvalues and eigenvectors of linear operators. In this research most of them originate in quantum physics, such as Schroedinger operators for individual particles or bulk matter, or the Skyrme model for baryons. The principal investigators will continue their work on these and other subjects by combining abstract techniques, primarily from functional analysis, with more particular tools, e.g. from the theory of differential equations or perturbation techniques. Intuition from physics and from numerical calculations is also expected to help.