Justification of the single-mode approximation for a finite-duration laser pulse interacting with an electron

The interaction Hamiltonian of an electron and a quasi-monochromatic pulse of a strong quantized electromagnetic field is examined. Canonical transformations of the field variables are found that allow the division of the system's Hamiltonian in two parts. The first one describes the interaction between an electron and a single collective mode of the field. The properties of this mode are defined by the superposition of the modes corresponding to the pulse wave packet. The second part describes the field fluctuations relatively to the collective mode. The field intensity, pulse duration and transversal spread are estimated for which a single-mode approximation can be used for the system's description