  A quantitative description of magnons in long-range ordered quantum
antiferromagnets is presented which is consistent from low to high energies. It
is illustrated for the generic $S=1/2$ Heisenberg model on the square lattice.
The approach is based on a continuous similarity transformation in momentum
space using the scaling dimension as truncation criterion. Evidence is found
for significant magnon-magnon attraction inducing a Higgs resonance. The
high-energy roton minimum in the magnon dispersion appears to be induced by
strong magnon-Higgs scattering.
