论文标题
从格拉曼（Grassmann）补充到霍奇·偶尔
From Grassmann complements to Hodge-duality
论文作者
论文摘要
霍奇二元性是20世纪代数和分析几何形状的中心概念，在最近的数学物理学中也起着不可忽略的作用。乍一看，人们可能会期望它的起源在1930年代，当时它的名字供名人员威廉·V.D（William V.D.）霍奇，开始了他的数学研究。另一方面，霍奇（Hodge）的理论与麦克斯韦方程式之间的紧密联系有时不仅是从系统的角度来看，而且从历史上讲也是如此。在将古典电磁学转变为相对论麦克斯韦理论的过程中，格拉斯曼交替产品的影响和他称为“补体”的操作发挥了一定的作用。实际上，格拉斯曼（Grassmann）的“补充”是后来的霍奇之星操作的线性代数模板。本文调查了从格拉曼的补充及其在相对论电动力学中的外观到霍奇的谐波形式理论。
Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical physics. At first sight one might expect that its origins lie in the 1930s when its name-giving protagonist, William V.D. Hodge, started his mathematical research. On the other hand, a close link between Hodge's theory and the Maxwell equation has sometimes been claimed not only from a systematic point of view but also historically. In the transformation of classical electromagnetism to the relativistic Maxwell theory the influence of Grassmann's alternating product and an operation he called "complement" played a certain role. In fact, Grassmann's "complements" were a linear algebraic template of the later Hodge star operation. This paper surveys the development from Grassmann's complements and their appearance in relativistic electrodynamics to Hodge's theory of harmonic forms.
