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

巴特尔教授的研究涉及到在量子场论中使用小波分析。在这个项目中，他将致力于三维时空中旋量量子电动力学的红外问题，以及群值Sigma模型的紫外位相细胞分析。数学物理的许多事业都涉及对函数空间的分析，通常是由几个位置和动量变量组成的函数。这些函数表示正在建模的任何物理系统的可能状态。模型的属性通过从这些函数中提取数字或将其转换为其他函数的过程进行编码。在研究这些过程时，一个有用的通用数学方法是用无穷级数展开，这些级数的各个项在某种意义上是基本的，也是很容易理解的。基本术语参考顺序的选择取决于上下文和目标。例如，在这里研究的模型中，在规模变化下会发生什么是一个重要的考虑因素。巴特尔教授使用一种名为小波分析的策略来产生具有良好重新缩放行为的扩展。他的项目包括将这一系列技术应用于数学物理中的困难问题。

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.