对场与对场、偶场与奇场与电磁学
Pair and Impar, Even and Odd Form Fields and Electromagnetism
摘要：
本文在回顾了Schouten和de Rham关于损微分形式域和对微分形式域的定义后，（不要与偶数级和奇数级的微分形式场混淆）我们证明了在相对论时空中，（尽管有相反的主张）连贯地表达电磁学（我们相信任何其他物理理论）只使用对形式场，或者，如果愿意，以适当的方式一起使用对和损害形式场。这两种不同的描述只涉及数学选择，如果适当注意，似乎不会导致任何可观察到的物理后果。此外，我们还详细地证明了，在Clifford丛微分形式中的电磁理论公式，即所谓自由度规方法的两个麦克斯韦方程组成为一个方程时，与上述两种电磁理论公式是相容的。此外，我们直接从麦克斯韦方程推导力的密度（耦合的电磁场与充电电流），这是一个假设，在自由度规的方法来电磁。我们还记得麦克斯韦方程组的工程版本的公式，其使用电场和磁场作为相同性质的对象，即，而不使用极向量和轴向量。
英文摘要：
In this paper after reviewing the Schouten and de Rham definition of impair and pair differential form fields (not to be confused with differential form fields of even and odd grades) we prove that in a relativistic spacetime it is possible (despite claims in contrary) to coherently formulate electromagnetism (and we believe any other physical theory) using only pair form fields or, if one wishes, using pair and impair form fields together, in an appropriate way. Those two distinct descriptions involve only a mathematical choice and do not seem to lead to any observable physical consequence if due care is taken. Moreover, we show in details that a formulation of electromagnetic theory in the Clifford bundle formalism of differential forms where the two Maxwell equations of the so called free metric approach becomes a single equation is compatible with both formulations of electromagnetism just mentioned above. Moreover we derive directly from Maxwell equation the density of force (coupling of the electromagnetic field with the charge current) that is a postulate in the free metric approach to electromagnetism. We recall also a formulation of the engineering version of Maxwell equations using electric and magnetic fields as objects of the same nature, i.e., without using polar and axial vectors.
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