Spin change of Fermions and quantum energy spectrum

[claymine]

Okay i was reading abrikosov's book and he said since in QM spin only changes by integer values boson excitiation happens one at a time and fermion ALWAYS appears or disappears in pairs. but isn't change from a spin up to spin down 1/2 to -1/2? or i had the wrong convention which |1/2| shouldve been the story?

Thank you

 

[vanhees71]

I guess, what's meant is that in the creation of particles a spin-1/2 fermion can only be created in pairs, because otherwise you'd change the total angular momentum of the system by a half-integer value, which however is impossible due to the angular-momentum algebra (i.e., the su(2)-Lie algebra).

Of course there's nothing that prevents the spin flip from 1/2 to -1/2 of a single spin-1/2 fermion.