A detailed analysis of the photon emission spectra of an electron scattered
by a laser pulse containing only very few cycles of the carrying
electromagnetic field is presented. The analysis is performed in the framework
of strong-field quantum electrodynamics, with the laser field taken into
account exactly in the calculations. We consider different emission regimes
depending on the laser intensity, placing special emphasis on the regime of
one-cycle beams and of high laser intensities, where the emission spectra
depend nonperturbatively on the laser intensity. In this regime we in
particular present an accurate stationary phase analysis of the integrals that
are shown to determine the computed emission spectra. The emission spectra show
significant differences with respect to those in a long pulsed or monochromatic
laser field: the emission lines obtained here are much broader and, more
important, no dressing of the electron mass is observed.Comment: 31 pages, 15 figure
