Exact solutions for stimulated emissions by external sources

The exact solutions for transition amplitudes are derived for stimulated emissions by external sources. More precisely, we obtain the exact expressions for transition amplitudes for the emission of an arbitrary number of particles by the sources when some particles are already present, in the process, prior to the ''switching on'' of the external sources. The solutions are given for an arbitrary number of particles with arbitrary configurations (of momenta, spin, etc.) and for particles of spin-0, spin-1/2, massive and massless (photons) spin-1 particles, and massless (gravitons) spin-2 particles. Applications are given as illustrations to the process /PHI/→ anything, and, in quantum electrodynamics, to the process γ → e+ e- + any photons, in the presence of external sources, where a (virtual) photon decays into the pair e+ e-