洛伦兹力定律及其与隐藏动量、爱因斯坦-劳布力和阿哈罗诺夫-凯舍效应的联系
The Lorentz force law and its connections to hidden momentum, the Einstein-Laub force, and the Aharonov-Casher effect
摘要：
经典电动力学的洛伦兹力，当应用于磁性材料时，产生隐藏的能量和隐藏的动量。从坡印廷矢量、电磁动量密度、洛伦兹力和力矩密度中去除隐藏实体的贡献，简化了经典理论的方程。特别地，电磁力密度的简化表达式变得与电场和磁场施加在电荷、电流、极化和磁化分布上的力的爱因斯坦-劳布表达式非常相似（但不相同）。实例揭示了描述电磁场对材料介质施加的力和扭矩的各种方程之间的异同。爱因斯坦-劳布公式简化的一个重要例子是在静态电场中运动的磁偶极子，它表现出阿哈罗诺夫-卡希尔效应。
英文摘要：
The Lorentz force of classical electrodynamics, when applied to magnetic materials, gives rise to hidden energy and hidden momentum. Removing the contributions of hidden entities from the Poynting vector, from the electromagnetic momentum density, and from the Lorentz force and torque densities simplifies the equations of the classical theory. In particular, the reduced expression of the electromagnetic force-density becomes very similar (but not identical) to the Einstein-Laub expression for the force exerted by electric and magnetic fields on a distribution of charge, current, polarization and magnetization. Examples reveal the similarities and differences among various equations that describe the force and torque exerted by electromagnetic fields on material media. An important example of the simplifications afforded by the Einstein-Laub formula is provided by a magnetic dipole moving in a static electric field and exhibiting the Aharonov-Casher effect.
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