  We use series expansion methods to calculate the dispersion relation of the
one-magnon excitations for the spin-1/2 triangular-lattice nearest-neighbor
Heisenberg antiferromagnet above a three-sublattice ordered ground state.
Several striking features are observed compared to the classical (large-S)
spin-wave spectra. Whereas at low energies the dispersion is only weakly
renormalized by quantum fluctuations, significant anomalies are observed at
high energies. In particular, we find roton-like minima at special wave-vectors
and strong downward renormalization in large parts of the Brillouin zone,
leading to very flat or dispersionless modes. We present detailed comparison of
our calculated excitation energies in the Brillouin zone with the spin-wave
dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov
[cond-mat/0608002]. We find many common features but also some quantitative and
qualitative differences. We show that at temperatures as low as 0.1J the
thermally excited rotons make a significant contribution to the entropy.
Consequently, unlike for the square lattice model, a non-linear sigma model
description of the finite-temperature properties is only applicable at
extremely low temperatures.
