齐次麦克斯韦方程组与函数论的关系
The relations of the homogeneous Maxwell's equations to the theory of functions
摘要：
该论文开发的科尼利厄斯Lanczos在他的博士论文是，电动力学是一个纯粹的场论这是超解析代数的双四元数。在这个理论中，麦克斯韦的齐次方程对应于柯西-黎曼正则性条件对四个复变量的推广，以及麦克斯韦场中的电子对奇点的推广。由于在Lanczos电动力学中没有物质粒子，相同的作用原理适用于正则和奇异麦克斯韦场。因此，经典电动力学的通常作用积分不是该理论的输入，而是从应用汉密尔顿原理到两个或多个均匀麦克斯韦场叠加的结果。这导致一个完全一致的电动力学，而且，可以证明是有限的。作为副产品，这一显着的论文兰索斯预计莫西尔-Fueter理论的四元数解析函数超过十年，表明麦克斯韦方程是不变的自旋1和自旋1/2洛伦兹变换，即取代一个奇点到虚空间增加了一个内在的磁场，其电场;他的理论甚至包括引力--尽管不是以爱因斯坦的广义相对论形式，兰佐斯把他的论文献给了爱因斯坦。
英文摘要：
The thesis developed by Cornelius Lanczos in his doctoral dissertation is that electrodynamics is a pure field theory which is hyperanalytic over the algebra of biquaternions. In this theory Maxwell's homogeneous equations correspond to a generalization of the Cauchy-Riemann regularity conditions to four complex variables, and electrons to singularities in the Maxwell field. Since there are no material particles in Lanczos electrodynamics, the same action principle applies to both regular and singular Maxwell fields. Therefore, the usual action integral of classical electrodynamics is {not} an input in that theory, but rather a consequence which {derives} from the application of Hamilton's principle to a superposition of two or more homogeneous Maxwell fields. This leads to a fully consistent electrodynamics which, moreover, can be shown to be finite. As byproducts to this remarkable thesis Lanczos anticipated the Moisil-Fueter theory of quaternion-analytic functions by more than ten years; showed that Maxwell's equations are invariant in both spin-1 and spin-1/2 Lorentz transformations; that displacing a singularity into imaginary space adds an intrinsic magnetic-like field to its electric field; and that his theory does even include gravitation -- although not in the general relativistic form of Einstein to whom Lanczos dedicated his dissertation.
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