I am a bit confused about spin conservation at relativistic energies. I am reading a QFT book by Peskin and at a point he specifies that "In the nonrelativistic limit the total spin of the system is conserved". Later when we go to the non relativistic limit (there is the interaction between a photon and an electron this time), the spin is not conserved anymore (I attached a pic of what I mean).
So the spin is not always conserved? It is just the helicity? And what is the general statement (a conservation law shouldn't care about the energy at which the experiment takes place)? What is always conserved here? Moreover in the pic I attached he specifies that "the total spin angular momentum of the final state is one unit less than that of the initial state". I am not sure I understand. The spin doesn't point along the same direction before and after. I agree they have different values, but I am not sure I understand why it is a difference of 1? What is the common axis they use for both before and after? Thank you!