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I am studing elementary particle physics and want to ask something, just to check if I have understood properly. So, as I understand, this is true about four-momentum in special relativity:

1. The square of the sum of particles' four momenta is invariant under Lorentz transformations.

2. The four momentum is NOT invariant under Lorentz transformations.

3. The four momentum is conserved.

This seems to be extremely usefull in particle physics. I hope the statements are true. Are they? What about proving them? Where can I find proofs?