Use of the method of ordered operators in the theory of laser systems. Derivation of asymptotically exact equations for radiation. I

In the framework of Dicke type models, a theory of laser radiation of two-level systems is constructed. The theory uses the method of ordered operators, which makes it possible to eliminate the atomic variables and obtain an asymptotically exact (in the sense of the thermodynamic limit) hierarchy of equations for the mean values, which depend only on the variables of the radiation. We also consider the derivation of kinetic equations describing the radiation.