Spin component variance ($\mathrm{Var}(S_{\alpha })=⟨S_{\alpha }^2⟩-⟨S_{\alpha }{⟩}^2$)

The uncertainty of a spin projection is measured by its variance. In a maximally polarized spin coherent state, the longitudinal variance is zero and each transverse variance is $S/2$ in units $\hslash =1$. The transverse fluctuations do not imply finite magnon occupation in an isotropic ferromagnet's polarized vacuum.