Stimulated emission by external sources in quantum field theory

A formalism is developed to study stimulated emission by external sources in relativistic quantum field theory as a generalization of an earlier work involving essentially noninteracting particles. A general expression is derived for transition amplitudes for the production of an arbitrary number of particles, as final products, by emission sources when there is initially an arbitrary number of particles before the intervention of the emission sources, thus stimulating the latter for further emissions. An application to quantum electrodynamics is then given in the presence of an external electromagnetic current with an initial background radiation of an arbitrary number of photons with unspecified momenta and spins leading to an electron-positron pair as final products.