I am trying to learn Quantum mechanics and I am familiar with Pauli matrice but not with group theory. I want to understand SU2 symmetry in common language. When we talk about Pauli matrix x we simply say that it flips the spin. What SU2 symmetry does?What is the advantage of using SU2 symmetry? Can someone please explain this in simple language?
closed as unclear what you're asking by Alfred Centauri, John Rennie, Dvij Mankad, stafusa, Kyle Kanos Sep 18 '18 at 10:02
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The Pauli matrices turn up in a number of places. They're basically the Lie algebra of SO(3), the 3d rotation group. They're useful in QM to describe spin.
$SU(2)$ is isomorphic to $Spin(3)$ which is the double cover of $SO(2)$. This is helpful in describing 2-component spinors.
You might find it worthwhile working through Shankars book QM as he approaches the subject in a fairly straight-forward and transparent way.