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## Main Question or Discussion Point

I'm trying to prove that the helicity operator [itex]\pmb{\sigma}\cdot\pmb{\hat{p}}[/itex] is invariant under rotations. I found in Sakurai: Modern Quantum Mechanics page 166 that the Pauli matrices are invariant under rotations. Clearly that is sufficient for the helicity operator to be invariant under rotations. However I'm unable to prove that the Pauli matrices are invariant under rotations, and Sakurai states no proof. How would I prove this? I do know the fact that if U is the unitary matrix that represents rotation from n to n', then [itex]U(\pmb{\sigma}\cdot\pmb{n})U^\dagger=\pmb{\sigma}\cdot\pmb{n'}[/itex], however it doesn't seem to help.