Constructive Quantum Field Theory

这个项目的目标是在数学上严格地构建和研究量子场论模型。这将有助于理解基本粒子物理学，最终预测粒子质量、散射振幅等等。它还有助于研究许多身体系统的某些特性，特别是关键现象。具体要研究的模型如下：(1)。二维正弦-戈登模型。这是一个具有周期性相互作用的标量场。它也描述了经典的库仑气体。(2)三维和四维的phi-fourth模型。这些是具有四次自相互作用的标量场。(3)。三维量子电动力学。这是关于电子和光子的理论。(4)。杨·米尔斯的三维和四维。这是一个纯粹的非阿贝尔规范理论。

This project has as a goal the mathematically rigorous construction and study of quantum field theory models. This would be an aid to the understanding of elementary particle physics, ultimately predicting particle masses, scattering amplitudes, and so forth. It would also help in the study of some properties of many body systems, particularly critical phenomena. Specific models to be studied are the following. (1.) The Sine- Gordon model in 2 dimensions. This is a scalar field with a periodic interaction. It also describes a classical Coulomb gas. (2.) phi-fourth models in 3 and 4 dimensions. These are scalar fields with a quartic self-interaction. (3.) Quantum electrodynamics in 3 dimensions. This is the theory of electrons and photons. (4.) Yang Mills in 3 and 4 dimensions. This is a pure non- Abelian gauge theory.