Mathematical Sciences: Wavelets and Mathematical Physics

数学科学：小波和数学物理

• 批准号: 9024867
• 负责人: G Battle
• 金额: $ 3.91万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9024867&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Wavelets; Physics

Professor Battle will continue his work to construct nontrivial quantum field theories. In particular, this project will concentrate on the nonlinear sigma model, a strictly renormalizable asymptotically free theory. His technique of construction will use the relatively new concept of wavelet which he will develop to meet the particular requirements of quantum field theory. Quantum fields are the basic quantities which are thought to be responsible for all the interactions between particles which exist in nature. It is therefore notable that these objects which are essentially mathematical entities, have not been shown to exist. Professor Battle is one of the few mathematical physicists who work in the area of construction of quantum field theories. His project involves the construction of a model theory called the nonlinear sigma model. A side benefit of Battle's work is his use of wavelets in this construction. These objects have turned out to be of use in many other areas of pure and applied mathematics, and Battle has and will continue to contribute toward their development.

巴特尔教授将继续致力于构建非平凡的量子场论。 特别是，该项目将集中于非线性 sigma 模型，这是一种严格可重整的渐近自由理论。 他的构造技术将使用相对较新的小波概念，他将开发这种概念来满足量子场论的特殊要求。 量子场是被认为负责自然界中存在的粒子之间所有相互作用的基本量。 因此值得注意的是，这些本质上是数学实体的对象尚未被证明存在。 巴特尔教授是少数从事量子场论构建领域工作的数学物理学家之一。 他的项目涉及构建称为非线性西格玛模型的模型理论。 Battle 工作的一个附带好处是他在这个结构中使用了小波。 这些对象已被证明在纯数学和应用数学的许多其他领域都有用，巴特尔已经并将继续为它们的发展做出贡献。