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Since the Lagrangian of our quantum field theories is covariant under Lorentz transformations I'm asking myself if there is any link to some symmetries (like that we get from gauge transformations which also let the Lagrangian unchanged)? So is it possible to apply Noether's theorem to this invariance or doesn't this makes any sense? So what is the mathematically difference between this two transformations and their behavior?

Qmechanic
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Alpha001
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    Related: http://physics.stackexchange.com/q/12559/2451 and links therein. – Qmechanic Jun 02 '16 at 09:53
  • I don't understand what you're asking. The Lorentz transformations are symmetries of the Lagrangian, so you can of course apply Noether's theorem to them. What exactly is your question about that? – ACuriousMind Jun 02 '16 at 11:32

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The corresponding symmetry group is the Lorentz group and yes we can use Noether to derive conserved quantities:

  • Invariance under translations $\rightarrow$ momentum conservation
  • Invariance under rotations $\rightarrow$ spin and angular momentum conservation
  • Invariance under boost $\rightarrow$ some strange, not really useful, conserved quantity
Community
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jak
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    Sorry, it would be irrelevant; but are you the Jakob who wrote Physics from Symmetry? Don't worry; comment would be deleted :) –  Jun 02 '16 at 09:17
  • Please place a clear statement of your question. – Mass Jun 02 '16 at 09:23