Non-perturbative quantum time evolution on the light-front

We introduce a covariant, nonperturbative, first principles numerical approach for solving time-dependent problems in quantum field theory. We demonstrate this approach by evaluating photon emission from an electron in a strong, time and space dependent external field. We study the acceleration of the electron in combination with the evolution of the invariant mass of the electron-photon system, in real time and at the amplitude level. Successive excitations of the electron-photon system are evident.