Constructive Quantum Field Theory

0070905 Dimock这个项目的目标是研究具有完整数学严谨性的量子场论模型。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作用。具体目标如下。（一）三维环面上量子电动力学的构造。 这是朝着控制四维量子电动力学和/或四维量子色动力学迈出的一步，这两个在物理学中都是至关重要的。（2.）三维N分量标量场重整化群的非高斯不动点的构造。 这将是理解更广泛的临界现象的进步。（3.）格点上非阿贝尔规范场的Higgs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.