We investigate the dielectric response of a planar Bose plasma in the
presence of a constant external magnetic field. The conductivity tenso
r is derived in the self-consistent random-phase approximation. The te
nsor components are evaluated at zero temperature, leading to explicit
dispersion relations for the electrodynamic modes of the plasma. For
plasma layers, longitudinal and transverse modes are in general couple
d. These coupled modes are investigated in detail.