Dynamics of collective radiation of molecules

A model of the interaction of radiation with $N$ diatomic molecules is considered. The dynamics of the radiation is determined by the $N\to\infty$ asymptotic behavior of the matrix element of the evolution operator in the functional representation. The resonance and nonresonance approximations for dipole transitions between two electron levels of the molecule are investigated. In the resonance case allowance is made for the gauge invariance of the interaction by means of a constraint between the dynamical variables. The influence of the vibrational degrees of freedom on the radiation is discussed, and so is the condition for obtaining a resonance Maxwell–Bloch equation from the quantum dynamics that is “semiclassical with respect to the field”.