  This paper introduces "time-dependent basis light-front quantization", which
is a covariant, nonperturbative, and first principles numerical approach to
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.
