物理学导论中的势动量、规范理论和电磁学
Potential Momentum, Gauge Theory, and Electromagnetism in Introductory Physics
摘要：
如果势能是一个四维向量的类时分量，那么必然有一个相应的类空部分，逻辑上称之为势动量。由势动量和势能组成的势四动量，就是关联力的规范场乘以与该力关联的电荷。正则动量是普通动量和势能动量之和。物质波在规范场中的不连续性折射可以用来在初等水平上探索规范场的效应。使用这个工具，就可以说明电磁学的洛伦兹力定律是如何从规范理论推导出来的。由此产生的论点是学生在介绍微积分为基础的物理课程的水平和联系在一起的经典和量子力学，相对论，规范理论，电磁学。由此产生的经济演示使得它更容易包括现代物理学在一年的课程通常可用于教学介绍物理学。
英文摘要：
If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and the potential energy taken together is just the gauge field of the associated force times the charge associated with that force. The canonical momentum is the sum of the ordinary and potential momenta. Refraction of matter waves by a discontinuity in a gauge field can be used to explore the effects of gauge fields at an elementary level. Using this tool it is possible to show how the Lorentz force law of electromagnetism follows from gauge theory. The resulting arguments are accessible to students at the level of the introductory calculus-based physics course and tie together classical and quantum mechanics, relativity, gauge theory, and electromagnetism. The resulting economy of presentation makes it easier to include modern physics in the one year course normally available for teaching introductory physics.
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