  A nonperturbative method for the solution of quantum field theories is
described in the context of quantum electrodynamics and applied to the
calculation of the electron's anomalous magnetic moment. The method is based on
light-front quantization and Pauli-Villars regularization. The application to
light-front QED is intended as a test of the methods in a gauge theory, as a
precursor to possible methods for the nonperturbative solution of quantum
chromodynamics. The electron state is truncated to include at most two photons
and no positrons in the Fock basis, and the wave functions of the dressed state
are used to compute the electrons's anomalous magnetic moment. A choice of
regularization that preserves the chiral symmetry of the massless limit is
critical for the success of the calculation.
