On the description of a free-electron laser in a moving frame

We comment on the description of the standard free-electron laser in the Bambini-Renieri moving frame, whose significance is in the fact that the electron Hamiltonian is free from explicit time dependence. It is shown that this moving frame is essentially equal to the rest frame of the “resonant” electron (the electron whose motion is affected only by the wiggler field), a fact that apparently is not recognized.