# Spin: why su(2) for an electron

1. Sep 23, 2007

### plmokn2

Sorry if this is a silly question (I'm doing a fairly basic QM course but am doing a bit of extra reading for interest etc.), but why for an spin hbar/2 particle is the spin operators (the Pauli matricies) the generator of su(2)? I understand why generally generators act as conserved observables, and according to wikipedia su(2) is isomporphic to so(3) (which is plausible to me, even though the details are maybe beyond me, since both have the same number of independent variables and the generators commute in the same ways) but this doesn't explain why su(2) is used?

Any help appreciated.
Thanks