Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lorentz covariance and Noether's theorem

  1. Jul 23, 2012 #1


    User Avatar
    Gold Member

    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.
  2. jcsd
  3. Jul 23, 2012 #2


    User Avatar
    Science Advisor

    The conserved quantity is the angular momentum. Relativistically it's an antisymmetric tensor Jμν. See this recent thread.
  4. Jul 23, 2012 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
  5. Jul 23, 2012 #4


    User Avatar
    Science Advisor

    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook