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

  • Thread starter Bapelsin
  • Start date
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.
 
21
0
This and a lot more of that you can find in a book by Greiner called relativistic quantum mechanics. Good luck!
 

samalkhaiat

Science Advisor
1,572
715
I need help showing that the Euler-Lagrange equations are Lorentz invariant
Welcome to PF.
The E-L equations are statements derived covariantly from an invariant action integral. Therefore they are covariant with respect to Lorentz group.

(if Einstein's extended energy concept is used).
What is this, and what relation does it have with the Euler-Lagrange equations?


sam
 
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.
 

Attachments

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:

Want to reply to this thread?

"Show Lorentz invariance for Euler-Lagrange's equations- how?" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top