Holstein–Primakoff occupation constraint
= Holstein–Primakoff occupation constraint
{c}
{title2=$0\le a^\dagger a\le2S$}
A spin-$S$ <Hilbert space> has dimension $2S+1$. Its <Holstein–Primakoff transformation> therefore uses only bosonic <occupation numbers> $0,1,\ldots,2S$. The square root annihilates the upper endpoint. A truncated <linear spin-wave approximation> formally enlarges this space; it is self-consistent only when boson depletion is small compared with $S$.