  Using a self-consistent mean-field theory for the $S=1/2$ Heisenberg
antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for
the dispersion. It is exact in one dimension ($d=1$) and agrees well with
numerical results in $d=2$. With an expansion in powers of the inverse
coordination number $1/Z$ ($Z=2d$) we investigate if this expression can be
{\em exact} for all $d$. The projection method of Mori-Zwanzig is used for the
{\em dynamical} spin susceptibility. We find that the expression of Kr\"uger
and Schuck deviates in order $1/Z^2$ from our rigorous result. Our method is
generalised to arbitrary spin $S$ and to models with easy-axis anisotropy $\D$.
It can be systematically improved to higher orders in $1/Z$. We clarify its
relation to the $1/S$ expansion.
