Page:Grundgleichungen (Minkowski).djvu/41

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(75) ,

, u.s.f.

,

, u.s.f.

,

(76) ,

These quantities are all real. In the theory for bodies at rest, the combinations ( are known as Maxwell's Stresses", are known as the Poynting's Vector, as the electromagnetic energy-density, and L as the Langrangian function.

On the other hand, by multiplying the alternating matrices of f and F, we obtain

(77)

and hence, we can put

(78) ,

where by L, we mean L-times the unit matrix, i.e. the matrix with elements

Since here , we deduce that,

,

and find, since , we arrive at the interesting conclusion

(79) ,

i.e. the product of the matrix S into itself can be expressed as the multiple of a unit matrix — a matrix in which all the elements except those in the principal diagonal are zero, the elements in the principal diagonal are all equal