We present a formalism for the calculation of scattering amplitudes for electron-laser pulse processes. Our results make use of standard Feynman-Dyson $S$-matrix techniques and the Lehmann-Symanzik-Zimmermann reduction formalism. The laser pulse is described quantum mechanically as a coherent-state wave packet. The electron is represented by wave-packet solutions of the Dirac equation in the case of scattering boundary conditions, or by Volkov wave packets when we desire nonscattering boundary conditions. We demonstrate the existence of new, nonlinear corrections of a quantum-mechanical nature for the process of stimulated Compton scattering.

• Received 13 June 1974

DOI:https://doi.org/10.1103/PhysRevD.11.1639