Method of reduced description of coherent radiation

Basing on the Bogolubov fundamental idea of the hierarchy of relaxation times in the evolution of nonequilibrium processes, methods are considered of the reduced description of processes of coherent radiation. Connections as well as differences are demonstrated between the Bogolubov method of elimination of boson variables and the Zwanzig projection operator method. It is shown that for the one-photon superfluorescence and two-boson super-radiance the representation of the adiabatic switching-on of the interaction is valid. The system of two-level emitters with two-boson interaction of the cascade type is studied. The numerical solution shows that the two-boson super-radiance, in contrast to the one-photon one, has large delay time. Two-boson superfluorescence in the self-consistent field approximation taking into account spontaneous radiation is absent, which does not contradict the known equilibrium solutions.