Page:Grundgleichungen (Minkowski).djvu/34



The vector $$\Psi$$ is perpendicular to w; we can call it the Magnetic rest-force.

Relations analogous to these hold among the quantities $$iwF^{*},\mathfrak{M,E,w}$$ and Relation (D) can be replaced by the formula

We can use the relations (C) and (D) to calculate F and f from $$\Phi$$ and $$\Psi$$, we have

and applying the relation (45) and (46), we have

i.e.

Let us now consider the space-time vector of the second kind $$[\Phi \Psi]$$, with the components

Then the corresponding space-time vector of the first kind

vanishes identically owing to equations 49) and 53).

Let us now take the vector of the 1st kind

with the components

$$\Omega_{1}=-i\left|\begin{array}{ccc} w_{2}, & w_{3}, & w_{4}\\ \Phi_{2}, & \Phi_{3}, & \Phi_{4}\\ \Psi_{2}, & \Psi_{3}, & \Psi_{4}\end{array}\right|$$, etc.

Then by applying rule (45), we have