Mathematical Sciences: Quantum Electrodynamics in Three Space-Time Dimensions II

巴特尔教授的研究涉及小波的使用 量子场论中的分析在这个项目中，他将 旋量量子电动力学的红外问题 三个时空维度，在紫外线相位单元上， 分析组值sigma模型。 数学物理学的大部分事业都与 通过分析函数空间，通常是 几个位置和动量变量。这些函数表示 任何物理系统的可能状态。 模型的属性由获取 从这些函数中提取数字，或者将它们转换为 其他功能。一种通用的数学技术， 研究这些程序是在无限级数中展开， 个别术语在某种意义上是基本的和容易理解的。 基本术语参考顺序的选择取决于 背景和目标。在这里研究的模型中， 例如，在规模变化下发生的事情是一个重要的 考虑.巴特尔教授使用一种叫做小波的策略 分析以产生具有良好的重新缩放行为的扩展。他 该项目包括将这种技术应用于困难的 数学物理中的问题

Professor Battle's research involves the use of wavelet analysis in quantum field theory. In this project, he will work on the infrared problem for spinor quantum electrodynamics in three space-time dimensions, and on the ultraviolet phase cell analysis of group-valued sigma models. Much of the enterprise of mathematical physics is concerned with analysis on spaces of functions, typically functions of several position and momentum variables. The functions represent possible states of whatever physical system is being modeled. Properties of the model are encoded by procedures for getting numbers out of these functions, or for transforming them into other functions. A general mathematical technique useful in studying these procedures is to expand in infinite series whose individual terms are in some sense basic and well-understood. Choice of the reference sequence of basic terms depends on context and objectives. In the models being studied here, for instance, what happens under change of scale is an important consideration. Professor Battle uses a strategy called wavelet analysis to produce expansions with good rescaling behavior. His project consists in applying this body of technique to difficult problems in mathematical physics.