Scientific advances and several technical breakthroughs have led to
a remarkable increase in available laser intensities over the past
decades. In available ultra-intense laser fields, photon fluxes may
become so high that free charge carriers interact coherently with
several of the field's photons. In this thesis such nonlinear
interactions are investigated for the prime example of radiation
emission by electrons scattered from intense laser pulses of
arbitrary temporal structure. To this end, nonlinear quantum field
theory is employed taking the interaction with the laser into
account exactly. After an in-depth introduction to classical
particle dynamics as well as quantum field theory in nonlinearly
intense laser fields the emission of one and two photons is
explicitly analyzed. The results are then translated to viable
technical applications, such as a scheme for the determination of
the carrier-envelope phase of ultra-intense laser pulses and a
proposal for detecting the strongly suppressed two-photon signal.
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