  We introduce a nonperturbative, first principles numerical approach for
solving time-dependent problems in quantum field theory, using light-front
quantization. As a first application we consider QED in a strong background
field, and the process of non-linear Compton scattering in which an electron is
excited by the background and emits a photon. We track the evolution of the
quantum state as a function of time. Observables, such as the invariant mass of
the electron-photon pair, are first checked against results from perturbation
theory, for suitable parameters. We then proceed to a test case in the strong
background field regime and discuss the various nonperturbative effects
revealed by the approach.
