A rigorous quantum mechanical model for the process of collective spon
taneous emission (superradiance) is given. The model is based on a dam
ped Dicke laser model for an arbitrary number of modes of the radiatio
n field. A new result in the theory of one-parameter semigroups and th
eir generators enables us, to obtain irreversible equations of motion
for the macroscopic (i.e. classical) observables in the thermodynamic
limit on the matter side, including damping reservoir terms. With help
of these equations the influences of the reservoirs on the process ar
e clarified. Equations for the emitted intensity pulses are derived an
d the radiation properties as well as the connections to the experimen
ts and the literature are discussed.