plmokn2
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I’ve got a couple of conceptual questions on spin etc, and any help would be appreciated.
First of all reading books (eg. Sakuri) it seems like authors tend to show there’s a homomorphism between the groups SO(3) and SU(2) using Euler angles etc. I know the Pauli matricies act as generators for the group SU(2), so does this and the homomorphism automatically mean the Pauli matricies can be considered to be generators of infinitesimal rotations and so lead to a conservation law (spin)? Also why do books seem to do it this way around rather than showing an isomorphism between the generators of SO(3) and SU(2) (which I suspect exists)?
One more thing, if the Pauli matricies do act as generators of rotations why do we get both orbital angular momentum and spin, when it seems like there’s only really one unique set of generators, so why do we have the two conserved quantities: spin and orbital angular momentum?
Thanks in advance.
First of all reading books (eg. Sakuri) it seems like authors tend to show there’s a homomorphism between the groups SO(3) and SU(2) using Euler angles etc. I know the Pauli matricies act as generators for the group SU(2), so does this and the homomorphism automatically mean the Pauli matricies can be considered to be generators of infinitesimal rotations and so lead to a conservation law (spin)? Also why do books seem to do it this way around rather than showing an isomorphism between the generators of SO(3) and SU(2) (which I suspect exists)?
One more thing, if the Pauli matricies do act as generators of rotations why do we get both orbital angular momentum and spin, when it seems like there’s only really one unique set of generators, so why do we have the two conserved quantities: spin and orbital angular momentum?
Thanks in advance.