The external-field approximation in quantum optics

A canonical transformation is presented in which the effect of a coherent, classical, externally applied field (represented by a Glauber coherent state) is transferred from the boundary conditions to the hamiltonian, resulting in the addition of an external, classical field to the hamiltonian, while still retaining in it the effect of internal radiation fields in a second-quantized form. This procedure justifies the use of the external-field approximation in cases where internal-radiation effects have to be retained to all orders in the correlation functions. Examples of such cases are (a) radiative damping of a collision-broadened molecular sample and (b) long-range correlations in near-critical conditions where retardation effects prevail in the intermolecular forces.