Constructive Quantum Field Theory

这个项目的目标是研究完全数学严谨的量子场论模型。这有助于阐明量子场论的结构，增强其预测能力。量子场论主要是基本粒子物理学的理论，但它在经典统计力学中也有重要的作用。具体目标如下：(1)三维环面上量子电动力学的构造。这是朝着在四个维度上控制量子电动力学和/或量子色动力学迈出的一步，这两个维度在物理学中都具有核心重要性。三维N分量标量场热归一化群的非高斯不动点构造。这将是在理解更广泛的批评现象方面的进步。格子上非阿贝尔规范场的希格斯机制研究。希格斯机制是弱相互作用理论的一个重要特征。

0070905DimockThe goal of this project is to study quantum field theory modelswith full mathematical rigor. This is useful to clarify thestructure of quantum field theory, and to enhance itspredictive power. Quantum field theory is primarily a theoryof elementary particle physics, but it also has an importantrole to play in classical statistical mechanics. Specific goalsare as follows.(1.) A construction of quantum electrodynamicson a three dimensional torus. This is a step toward controlof quantum electrodynamics and/or quantum chromodynamics infour dimensions, both of central importance in physics.(2.) The construction of a non-Gaussian fixed point for therenormalization group for an N-component scalar field in threedimensions. This would be progress toward understanding a widerange of critical phenomena.(3.) A study of the Higgs mechanism for non-Abelian gauge fieldson a lattice. The Higgs mechanism is an important feature oftheories of the weak interactions.