Spin Observables: Defining Reference Axes

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intervoxel

What is the criterion to define the reference axes, since $S_x$, $S_y$ and $S_z$ correspond to different Pauli matrices?

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intervoxel

I found the answer: In the theory the ladder operators are defined as

S_{\pm} \equiv S_x \pm iS_y.

That is, they act on the z direction.