  We explore the magnetic excitations of the spin-1/2 triangular
antiferromagnet Ba3CoSb2O9 in its 120 degree ordered phase using single-crystal
high-resolution inelastic neutron scattering. Sharp magnons with no decay are
observed throughout reciprocal space, with a strongly renormalized dispersion
and multiple soft modes compared to linear spin wave theory. We propose an
empirical parametrization that can quantitatively capture the complete
dispersions in the three-dimensional Brillouin zone and explicitly show that
the dispersion renormalizations have the direct consequence that one to two
magnon decays are avoided throughout reciprocal space, whereas such decays
would be allowed for the unrenormalized dispersions. At higher energies, we
observe a very strong continuum of excitations with highly-structured intensity
modulations extending up at least 4x the maximum one-magnon energy. The
one-magnon intensities decrease much faster upon increasing energy than
predicted by linear spin wave theory and the higher-energy continuum contains
much more intensity than can be accounted for by a two-magnon cross-section,
suggesting a significant transfer of spectral weight from the high-energy
magnons into the higher-energy continuum states. We attribute the strong
dispersion renormalizations and substantial transfer of spectral weight to
continuum states to the effect of quantum fluctuations and interactions beyond
the spin wave approximation, and make connections to theoretical approaches
that might capture such effects. Finally, through measurements in a strong
applied magnetic field, we find evidence for magnetic domains with opposite
senses for the spin rotation in the 120 degree ordered ground state, as
expected in the absence of Dzyaloshinskii-Moriya interactions, when the sense
of spin rotation is selected via spontaneous symmetry breaking.
