| As a step in the development of a nonperturbative method for the solution of bound-state problems in quantum chromodynamics (QCD), the Pauli--Villars (PV) regularization scheme is applied to a calculation of the dressed-electron state and its anomalous magnetic moment in light-front-quantized quantum electrodynamics (QED) in Feynman gauge. The regularization is provided by heavy, negative-metric fields added to the Lagrangian. The light-front QED Hamiltonian then leads to a well-defined eigenvalue problem for the dressed-electron state expressed as a Fock-state expansion. The Fock-state wave functions satisfy coupled integral equations that come from this eigenproblem. A finite system of equations is obtained by truncation to no more than two photons and no positrons; this extends earlier work that was limited to dressing by a single photon. Numerical techniques are applied to solve the coupled system and compute the anomalous moment, for which we obtain agreement with experiment, within numerical errors. As part of the analysis, the one-photon truncation is reconsidered in detail, and we find that the PV regularization requires a second PV photon flavor to restore the chiral symmetry of the massless-electron limit and to provide for slowly varying dependence on the PV masses. We also discuss the prospects for application of the method to QCD. |
