Mathematical Sciences: Wavelets and Mathematical Physics

巴特尔教授将继续他构建非平凡量子场论的工作。特别地，这个项目将集中于非线性sigma模型，一个严格重整可渐近自由理论。他的构造技术将使用相对较新的小波概念，他将发展以满足量子场论的特殊要求。量子场被认为是自然界中存在的所有粒子之间相互作用的基本量。因此，值得注意的是，这些本质上是数学实体的对象并没有被证明存在。巴特尔教授是为数不多的从事量子场论构建工作的数学物理学家之一。他的项目涉及建立一个模型理论，称为非线性模型。巴特尔的工作的一个附带好处是他在这个结构中使用了小波。事实证明，这些对象在纯数学和应用数学的许多其他领域都是有用的，巴特已经并将继续为它们的发展做出贡献。

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.