离散量子电动力学
Discrete Quantum Electrodynamics
摘要：
本文的目的是构造一个适合于描述量子电动力学和Yang-Mills理论的量子场论，它满足Jaffe和Witten [12]所描述的克莱数学研究所所提供的千禧年奖的条件，证明它满足至少与Wightman [18]和Osterwalder和Schrader [14]所引用的公理一样强的公理，并且通过观察这种形式的场论没有质量间隙。这些定义为相对论量子力学提供了一个模型，它支持相对论量子场论的一种形式，但不依赖于“物质波”的二次量子化。波动力学的连续定律是在不涉及波或相互作用场的量子化的离散粒子相互作用模型中发现的。牛顿第一定律和动量守恒是从齐次性原理建立起来的。麦克斯韦方程组是从狄拉克粒子发射或吸收光子的简单相互作用导出的，表明重整化质量和耦合常数等于它们的裸值。费曼规则计算的离散理论，并给出标准重整化理论的预测。夸克约束相互作用描述qed和杨米尔斯理论的适应。
英文摘要：
The purpose of this paper is to construct a quantum field theory suitable for describing quantum electrodynamics and Yang-Mills theory in a form which satisfies the conditions of the Millennium prize offered by the Clay Mathematics Institute as described by Jaffe and Witten [12], by showing that it satisfies 'axioms at least as strong as those cited by' Wightman [18] and by Osterwalder and Schrader [14], and by observing that this form of field theory has no mass gap. The definitions provide a model for relativistic quantum mechanics which supports a form of relativistic quantum field theory, but which does not depend on the second quantisation of a 'matter wave'. Continuous laws of wave mechanics are found in model of discrete particle interactions which does not involve waves, or the quantisation of interacting fields. Newton's first law and conservation of momentum are established from the principle of homogeneity. Maxwell's equations are derived from the simple interaction in which a Dirac particle emits or absorbs a photon, showing that the renormalised mass and coupling constant are equal to their bare values. Feynman rules are calculated for the discrete theory and give the predictions of the standard renormalised theory. Quark confining interactions are described for qed and for an adaptation of Yang-Mills theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
