  We present the results of extensive molecular dynamics computer simulations
in which the high frequency dynamics of silica, nu>0.5 THz, is investigated in
the viscous liquid state as well as in the glass state. We characterize the
properties of high frequency sound modes by analyzing J_l(q,nu) and J_t(q,nu),
the longitudinal and transverse current correlation function, respectively. For
wave-vectors q>0.4 Angstrom^{-1} the spectra are sitting on top of a flat
background which is due to multiphonon excitations. In the acoustic frequency
band, i.e. for nu<20 THz, the intensity of J_l(q,nu) and J_t(q,nu) in the
liquid and the glass approximately proportional to temperature, in agreement
with the harmonic approximation. In contrast to this, strong deviations from a
linear scaling are found for nu>20 THz. The dynamic structure factor S(q,nu)
exhibits for q>0.23 Angstrom^{-1} a boson peak which is located nearly
independent of q around 1.7 THz. We show that the low frequency part of the
boson peak is mainly due to the elastic scattering of transverse acoustic modes
with frequencies around 1 THz. The strength of this scattering depends on q and
is largest around q=1.7 Angstrom^{-1}, the location of the first sharp
diffraction peak in the static structure factor. By studying S(q,nu) for
different system sizes we show that strong finite size effects are present in
the low frequency part of the boson peak in that for small systems part of its
intensity is missing. We discuss the consequences of these finite size effects
for the structural relaxation.
