Quantum effects in spontaneous and stimulated Compton laser-beam
interactions are considered in the frame of the Klein–Gordon
theory. We derive a quantum kinetic equation to describe the laser
cooling of electron beams. Nonlinear theory of coherent π-pulse
generation in the quantum X-ray Compton FEL is presented. A scheme of
coherent stimulated annihilation of electron-positron pairs and
stimulated emission of γ-ray photons is proposed.