Lorentz covariance and Noether's theorem

[ShayanJ]

Not sure its in the right place or not.If its not,sorry.

The relativity postulate of special relativity says that all physical equations should remain invariant under lorentz transformations And that includes Lagrangian too.
So it seems we have a symmetry(which is continuous),So by Noether's theorem,there should be a conserved quantity associated with it but I can't find what is that.

 

[Bill_K]

The conserved quantity is the angular momentum. Relativistically it's an antisymmetric tensor J_μν. See this recent thread.

 

[bcrowell]

The conserved quantity is the angular momentum. Relativistically it's an antisymmetric tensor J_μν. See this recent thread.

Here http://math.ucr.edu/home/baez/boosts.html is a discussion of the topic that focuses more directly on the boosts, as opposed to the rotations. Charles Torre's post near the bottom talks about how the distinction between boosts and rotations is not Lorentz-invariant. But putting aside this issue, I think it's fair to say that the boosts relate more directly to the center of mass, not to angular momentum, although the center of mass is part of what's described by the angular momentum tensor.

Another discussion: http://physics.stackexchange.com/questions/12559/what-conservation-law-corresponds-to-lorentz-boosts

 

[tom.stoer]

You should better look at Poincare invariance which results in conserved quantities for spatial rotations (angular momentum), boosts (boosts ?) and energy / momentum (time / space translation).