I've read in this paper (doi:10.1038/nature07871) that in the context of quantum mechanics, $\rm SU(2)$ symmetry leads to the conservation of spin polarization, or in other words invariance with respect to the rotation of the electron’s spin leads to such conservation. I'm very new to the subject, hence, my question is, what exactly does one mean with invariance with respect to the rotation? Most importantly, how can I picture/ draw in my mind ( if possible at all) the statement " invariance with respect to the rotation of the electron’s spin"?
My question is derived from this specific part of the paper.
"According to Noether’s theorem1, for every symmetry in nature there is a corresponding conservation law. For example, invariance with respect to spatial translation corresponds to conservation of momentum. In another well-known example, invariance with respect to rotation of the electron’s spin, or $\rm SU(2)$ symmetry, leads to conservation of spin polarization. For electrons in a solid, this symmetry is ordinarily broken by spin–orbit coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that $\rm SU(2)$ can be achieved in a two-dimensional electron gas, despite the presence of spin–orbit coupling2."