The Quantum Mechanical Many-Body Problem and Statistical Mechanics

在该奖项下的工作将解决多体系统的物理和数学中的基本问题。将有三个主要领域：(1)发展一种非微扰量子电动力学，可以适当地处理原子和凝聚态物理的束缚态；(2)在严格理解低密度玻色气体的基态方面取得的进展的延续，特别是凝结现象，这是一个当前非常感兴趣的实验主题；(3)哈伯德模型的研究，该模型现在被认为是相关电子现象的基石之一。此外，一些主题在纯数学和偏微分方程将被解决。

The work that will be done under this award addresses fundamental problems in the physics and mathematics of many-body systems. There will be three main areas: (1) the development of a non-perturbative quantum electrodynamics that can deal properly with the bound states of atomic and condensed matter physics; (2) a continuation of the progress made recently to understand rigorously the ground states of low density Bose gases, especially the condensation phenomenon, which is a subject of much current experimental interest; (3) the study of the Hubbard model, which is now considered one of the cornerstones of correlated electron phenomena. Additionally, some topics in pure mathematics and partial differential equations will be addressed.