if we write this in a vectorial way, we have:
(5a)
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Canceling index 3, we write which we obtained:
and introduce instead of and , composed from them by rule (1a). Then we have:
(6)
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that is, a composed of a and a .
We obtain another , by permutation of by in expressions (6). To demonstrate this, we form the two :
and
Multiplying them respectively with :
and
and summing, we construct from :
that can be written:
When we introduce by means of , then this is resulting in formulas analogous to (6):
(6a)
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where and have changed their place.
In the electrodynamics of Minkowski, four take part, i.e, the electric and magnetic excitations and , and two auxiliary vectors and , which form two :
and
Then we have the -"velocity"
( designates the three-dimensional velocity vector related to the speed of light).
If we combine this with according to scheme (6a), then we obtain the
(7)
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which were denoted by Minkowski as the "electric rest force". Instead, from the -"velocity"