According to the Wikipedia page about the Poincaré group, we get 10 conservation laws using Noethers theorem.
10 generators (in four spacetime dimensions) associated with the Poincaré symmetry, by Noether's theorem, imply 10 conservation laws:
1 for the energy – associated with translations through time
3 for the momentum – associated with translations through spatial dimensions
3 for the angular momentum – associated with rotations between spatial dimensions
3 for the velocity of the center of mass – associated with hyperbolic rotations between each spatial dimension and time
It seems to me that these reduce to just 7 conservation laws. Because velocity conservation of the center of mass is equivalent to momentum conservation. But why would 10 distinct symmetries only yield 7 distict conservation laws? Am I missing something?
