Constructive Quantum Field Theory

该项目以严格的数学构造和研究量子场论模型为目标。这将有助于理解基本粒子物理学，最终预测粒子质量、散射幅度等。它还将有助于研究许多身体系统的一些性质，特别是临界现象。要研究的具体模型如下。(1.)二维的Sine-Gordon模型。这是一个具有周期性相互作用的标量场。它还描述了一种经典的库仑气体。(2)PHI-三维和四维的第四个模型。这些是具有四次自作用的标量场。(3)三维量子电动力学。这就是电子和光子的理论。(4)杨在三维和四个维度上磨坊。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.