Page:Grundgleichungen (Minkowski).djvu/40

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§ 13. The Product of the Field-vectors fF.

Finally let us enquire about the laws which lead to the determination of the vector w as a function of x, y, z, t. In these investigations, the expressions which are obtained by the multiplication of two alternating matrices

are of much importance. Let us write.


Then (71)


Let L now denote the symmetrical combination of the indices 1, 2, 3, 4, given by


Then we shall have


In order to express in a real form, we write