关于经典电动力学中的“规范重整化”
On "gauge renormalization" in classical electrodynamics
摘要：
本文讨论了用齐次麦克斯韦方程组进行对称化规范变换，而用非齐次麦克斯韦方程组得到带电粒子系统的运动方程时，从正则形式导出对称电磁能量-动量张量的矛盾性。将适当的非齐次麦克斯韦方程应用于这两种操作，我们揭示了张量中的额外对称项，称为“补偿项”。通过分析这个“补偿项”的结构，我们提出了一种“规范重整化”的方法，它可以将经典电动力学中的发散项（无穷大的自力、自能和自动量）转化为收敛积分。非辐射带电粒子的运动方程不包含其自身力，质量参数包含机械质量和电磁质量之和。辐射粒子的运动方程也包含机械质量和电磁质量的总和，并且不产生任何“逃逸解”。研究表明，自由电磁场中的能流由坡印廷矢量引导，而束缚电磁场中的能流由本文定义的广义Umov矢量描述。“庞加莱应力”的问题也进行了研究。结果表明，电磁能量-动量张量中的“补偿项”的存在使得“4/3问题”得以解决，其中电子的总可观测质量完全由庞加莱应力决定，从而恢复了能量和动量之间的传统相对论关系。
英文摘要：
In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy-momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell equation to both operations, we have revealed an additional symmetric term in the tensor, named as "compensating term". Analyzing the structure of this "compensating term", we suggested a method of "gauge renormalization, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any "runaway solutions". It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov vector, defined in the paper. The problem of "Poincare stresses" is also examined. It has been shown that the presence of the "compensating term" in the electromagnetic energy-momentum tensor allows a solution of the "4/3 problem", where the total observable mass of the electron is completely determined by the Poincare stresses and hence the conventional relativistic relationship between the energy and momentum is recovered.
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