Hello! I'm currently going through(adsbygoogle = window.adsbygoogle || []).push({}); The Classical Theory of Fields-Landau, Lifshitzand I needed a bit of help on some of the math going on in a certain section.

The book can be found here https://archive.org/details/TheClassicalTheoryOfFields

On page 27, they give the action as:

[itex]\delta S = -mc \delta \int\limits_a^b ds =0[/itex]

With [itex]ds^2 = dx_i dx^i[/itex]. The definition of [itex]ds[/itex] does not bother me, but the steps they then take are very odd and I'm not quite sure how they obtain the equation before 9.10. If anyone could help that would be awesome!

If anyone doesn't want to open that PDF here is the line I'm speaking of, which they basically jump right into without explanation (it is assumed knowledge):

[itex]\delta S = -mc \int\limits_a^b \frac{dx_i \delta dx^i}{\sqrt{ds}}=-mc \int\limits_a^b u_i d\delta x^i[/itex]

Where [itex]u_i = \frac{dx_i}{ds}[/itex].

Thanks!

EDIT: I guess this should have been posted in the Relativity subforum, whoops.

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# Relativistic Action: Mathematics

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