Qin Hong, Burby Joshua W, Davidson Ronald C
Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543, USA.
Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):043102. doi: 10.1103/PhysRevE.90.043102. Epub 2014 Oct 6.
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
人们普遍认为，物理系统的能量 - 动量守恒是时空对称性的结果，这是一个基本原理。然而，对于经典粒子 - 场系统，例如通过自洽电磁场或静电场相互作用的带电粒子，这种联系只是被谨慎地提出，尚未正式确立。困难在于粒子动力学和电磁场存在于不同的流形上。我们展示了如何克服这一困难，并通过将场论的核心组成部分欧拉 - 拉格朗日方程推广到所谓的弱形式来建立这种联系。弱欧拉 - 拉格朗日方程诱导出一种新型的通量，称为弱欧拉 - 拉格朗日流，它进入守恒定律。结合这里发展的场论和弱欧拉 - 拉格朗日方程，可以从潜在的时空对称性系统地推导出用其他方法难以找到的能量 - 动量守恒定律。
