# Show Lorentz invariance for Euler-Lagrange's equations- how?

1. Mar 3, 2008

### Bapelsin

Hello,

I need help showing that the Euler-Lagrange equations are Lorentz invariant (if Einstein's extended energy concept is used). Is there an easy way to show this? Any help would be very much appreciated.

2. Mar 3, 2008

### Gigi

This and a lot more of that you can find in a book by Greiner called relativistic quantum mechanics. Good luck!

3. Mar 3, 2008

4. Mar 8, 2008

### Bapelsin

Gigi: Thanks for your tip, but I don't think I can obtain that book soon enough. But maybe later. :-)

samalkhaiat: Thank you! First of all I want to tell you that I am more or less a layman when it comes to this (I haven't studied natural sciences for almost three years, and I'm I only half-way to obtain a MSc degree in engineering physics) so I'm not sure I'm following you completely. So covariances and tensors and even less group theory etc. isn't my strong side. This was originally supposed to serve as a short background for a philosophical paper in science theory.

My physics professor tells me I'm right concerning this, but I don't know how to show this. As I don't know how to insert formulas here, I'm attaching the relevant ones as .GIF images. By extended energy concept I simply mean the famous formula E = mc².

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5. Mar 8, 2008

### Bapelsin

I forgot to mention that my main problem is that I don't know how a Lorentz' transformation in generalized coordinates look like. I've only dealt with such in Cartesian coordinates (Google etc. doesn't help me out much at all with this).

Last edited: Mar 8, 2008