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The realization of a Free Electron Laser (FEL) operating in the quantum regime could provide a compact and monochromatic X-ray source. In this thesis we de- veloped a three dimensional (3D) quantum theory for a FEL with a laser wiggler, based on a discrete Wigner function formalism taking into account the longitudi- nal momentum quantization. Starting from the exact quantum treatment, a mo- tion equation for the Wigner function coupled with self-consistent radiation field is derived in the realistic limit in which the normalized electron beam emittance is much larger than the Compton...