  We use quantum Monte Carlo simulations and numerical analytic continuation to
study high-energy spin excitations in the two-dimensional S=1/2 Heisenberg
antiferromagnet at low temperature. We present results for both the transverse
and longitudinal dynamic spin structure factor S(q,w) at q=(pi,0) and
(pi/2,pi/2). Linear spin-wave theory predicts no dispersion on the line
connecting these momenta. Our calculations show that in fact the magnon energy
at (pi,0) is 10% lower than at (pi/2,pi/2). We also discuss the transverse and
longitudinal multi-magnon continua and their relevance to neutron scattering
experiments.
