Page:Grundgleichungen (Minkowski).djvu/38

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(66)

If is a space-time vector of the 1st kind, then

(67)

In case of a Lorentz transformation , we have

,

i.e., lor s is an invariant in a {sc|Lorentz}}-transformation.

In all these operations the operator lor plays the part of a space-time vector of the first kind.

If f represents a space-time vector of the second kind, -lor f denotes a space-time vector of the first kind with the components

So the system o£ differential equations (A) can be expressed in the concise form

{A}

and the system (B) can be expressed in the form

{B}

Referring back to the definition (67) for , we find that the combinations and vanish identically, when f and F* are alternating matrices. Accordingly it follows out of (A), that

(68) ,