  Hamiltonian light-front quantum field theory provides a framework for
calculating both static and dynamic properties of strongly interacting
relativistic systems. Invariant masses, correlated parton amplitudes and
time-dependent scattering amplitudes, possibly with strong external
time-dependent fields, represent a few of the important applications. By
choosing the light-front gauge and adopting an orthonormal basis function
representation, we obtain a large, sparse, Hamiltonian matrix eigenvalue
problem for mass eigenstates that we solve by adapting ab initio no-core
methods of nuclear many-body theory. In the continuum limit, the infinite
matrix limit, we recover full covariance. Guided by the symmetries of
light-front quantized theory, we adopt a two-dimensional harmonic oscillator
basis for transverse modes that corresponds with eigensolutions of the
soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from
light-front holography. We outline our approach and present results for
non-linear Compton scattering, evaluated non-perturbatively, where a strong and
time-dependent laser field accelerates the electron and produces states of
higher invariant mass i.e. final states with photon emission.
