Mathematical Sciences: Spectral and Variational Problems of Mathematical Physics

这个数学研究项目将进行光谱 和变分分析的几个主题起源于 理论物理学 它既是纯数学又是应用数学： 应用在这个意义上，其中一个目标是 一个物理学家可以实际使用的公式， 就是证明严格的定理 身体上重要的东西往往是最小化者 某些泛函或特征值和特征向量的线性 运营商 在本研究中，大多数的量子力学起源于量子力学， 物理学，如单个粒子的薛定谔算子 或者是体物质，或者是重子的Skyrme模型。 校长 调查人员将继续他们的工作，这些和其他 通过结合抽象技术，主要从 功能分析，使用更特殊的工具，例如， 微分方程理论或微扰技术。 来自物理和数值计算的直觉也是 期待帮助。

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.