Interacting collective modes in a laser cavity

We define collective operators for the quantized radiation field in a one-dimensional laser cavity coupled to a semi-infinite outside region, and we consider the overlaps of neighboring collective modes to show how they modify, in the linear approximation, the time evolution of the radiation field below threshold. The model and procedure work directly within a continuous spectrum of modes and allow us to get an improved insight on the prescription for the laser field in single-mode operation.