麦克斯韦方程组的一些变式
Some Variations on Maxwell's Equations
摘要：
在这篇文章的第一部分，我们讨论了两个变化的麦克斯韦方程组，已在早期的工作-一类非线性麦克斯韦理论与明确的伽利略限制（和相应的广义杨米尔斯方程），和线性修改的动机耦合的电磁势与一定的非线性薛定谔方程。在最后一节中，我们将重温洛伦兹的一个旧思想，写出麦克斯韦方程组，以证明这样一种理论：同性电荷之间的排斥静电力与异性电荷之间的吸引静电力的大小根本不同。我们详细阐述了洛伦兹的描述，通过电和磁场强度，其控制方程分为两个完全相对论性的麦克斯韦系统-一个描述普通的电磁，和其他描述一个普遍的吸引力或排斥力的长程力。如果这样的力不能被已知的物理原理{ \it a priori}排除，那么它的大小应该通过实验来确定或界定。如果它真的存在，那么有趣的可能性就超出了洛伦兹早期关于它与（牛顿）引力的关系的猜想。
英文摘要：
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.
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