  We present a nonperturbative, first-principles numerical approach for
time-dependent problems in the framework of quantum field theory. In this
approach the time evolution of quantum field systems is treated in real time
and at the amplitude level. As a test application, we apply this method to QED
and study photon emission from an electron in a strong, time-dependent external
field. Coherent superposition of electron acceleration and photon emission is
observed in the nonperturbative regime.
