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?
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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
