  We consider the bremsstrahlung surface photon emissivity of strange quark
stars, by sistematically taking into account the effects of the multiple
scatterings of the highly relativistic quarks in a dense medium (the
Landau-Pomeranchuk-Migdal effect). Due to interference between amplitudes of
nearby interactions, the bremsstrahlung emissivity from strange star surface is
suppressed for frequencies smaller than a critical frequency. The range of the
suppressed frequencies is a function of the quark matter density at the star's
surface and of the QCD coupling constant. For temperatures much smaller than
the Fermi energy of the quarks the bremsstrahlung spectrum has the same
temperature dependence as the equilibrium black body radiation. Multiple
collisions could reduce the intensity of the bremsstrahlung radiation by an
order of magnitude. The effect of the thin electron layer at the surface of the
quark star on the bremsstrahlung spectrum is also analyzed in detail. It is
shown that absorption in the semi-degenerate electron gas can also
significantly reduce the intensity of the quark-quark bremsstrahlung radiation
and, consequently, the surface emissivity. Hence the combined effects of
multiple collisions and absorption in the electron layer could make the soft
photon surface radiation of quark stars six orders of magnitude smaller than
the equilibrium black body radiation.
