Holstein Primakoff representation in textbooks is defined by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\hat{S}^+_m=\sqrt{2S}\sqrt{1-\frac{\hat{B}_m^+\hat{B}_m}{2S}}\hat{B}_m[/tex]

[tex]\hat{S}_m^-=(\hat{S}^+_m)^+[/tex]

[tex]\hat{S}_m^z=S-\hat{B}_m^+\hat{B}_m[/tex]

And in practical cases it is often to use binomial series for square root, and condition for that is

##\frac{ \langle \hat{B}_m^+\hat{B}_m \rangle}{2S}<<1 ## and because of that I can use binomial series only in case ##S>>\frac{1}{2}##. However, it is very often to use that in case ##S=\frac{1}{2}## in papers. Any explanation?

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# Holstein Primakoff representation

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