High-Intensity Quantum Electrodynamics. I. Intensity Dependences for Feynman Diagrams

The prescriptions for evaluating Feynman diagrams in quantum electrodynamics are extended to the regime of incident photon beams having nonzero intensity. This is done both for the time-dependent formulation of the $S$-matrix perturbation theory, and for the stationary-state Brillouin-Wigner perturbation development. The results are applicable to a theory of any boson field, as they depend only on the Bose-Einstein commutation properties of the field operators; no restrictions are made on the nature of the interaction Hamiltonian. It is shown that, as far as radiative corrections are concerned, the presence of the incident beam is to be ignored; it is to be manifested by a weighting factor which depends on the count of only external photon lines connected to the scatterer line. The distribution of the incident photons over modes of the radiation field is completely arbitrary, and the results are valid to all orders in the perturbation theory.