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?
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2$\begingroup$ possible duplicate: Queries about rotational groups $\mathrm{SO}(3)$ and $\mathrm{SU}(2)$ in QM. $\endgroup$– AccidentalFourierTransformCommented Sep 17, 2018 at 2:11
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1$\begingroup$ Welcome New contributor herry! I've down-voted your question for the reason that it is unclear. I've also voted to close your question for the reason that it is unclear what you're asking. Please clarify your specific problem or add additional details to highlight excactly what you need. As it's currently written, it's hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. $\endgroup$– Alfred CentauriCommented Sep 17, 2018 at 2:12
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1$\begingroup$ Possible duplicate of Queries about rotational groups $\mathrm{SO}(3)$ and $\mathrm{SU}(2)$ in QM $\endgroup$– stafusaCommented Sep 17, 2018 at 11:15
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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.
answered Sep 17, 2018 at 2:08