Internal photon lines associated with the density matrix operator

Previous diagrammatic analyses of the density matrix are extended to incorporate quantum-electrodynamic processes fully by inclusion of the photon propagator and its complex conjugate. It is shown that eight fundamental time-ordered diagrams are necessary to describe radiative processes completely. For each of these, inclusion of the photon propagator permits, in addition to polarization, a direct calculation of electric field expectation values. Electric field correlations associated with the fundamental diagrams lead to a diagrammatic (quantum-electrodynamic) interpretation and derivation of the spontaneous emission limited linewidth associated with simulated emission as given by the Townes-Schawlow line narrowing formula. Stimulated Raman scattering, two-wave mixing, and parametric amplification are illustrative of the extension of these diagrammatic techniques to nonlinear optical phenomena