  This work is the first check of gauge invariance for nonperturbative
calculations in light-front QED. To quantize QED in an arbitrary covariant
gauge, we use a light-front analog of the equal-time Stueckelberg quantization.
Combined with a Pauli-Villars regularization, where massive, negative-metric
photons and fermions are included in the Lagrangian, we are then able to
construct the light-front QED Hamiltonian and the associated mass eigenvalue
problem in a Fock-space representation. The formalism is applied to the
dressed-electron state, with a Fock-space truncation to include at most one
photon. From this eigenstate, we compute the anomalous magnetic moment. The
result is found to be gauge independent, to an order in $\alpha$ consistent
with the truncation.
