Multiple Production of Photons in Quantum Electrodynamics

A formalism intended to evaluate the expectation value of physical quantities directly has been applied to the processes involving multiple production of photons in quantum electrodynamics. This has been achieved by constructing the Green's function which is done by expanding it in terms of hard and soft photon parts of the electromagnetic field. A general treatment of infrared divergence is given. The cross section for $n$-photon production in Coulomb scattering and pair annihilation has been evaluated. The limitation of the expansion of the Green's function in terms of hard and soft photon parts is examined. A plausible generalization regarding the cross section of any primary process in quantum electrodynamics at high energies with $n$-photon emission in the final state is enunciated.