Nonperturbative renormalization and the electron's anomalous moment in large-alpha QED

We study the physical electron in quantum electrodynamics expanded on the light-cone Fock space in order to address two problems: (1) the physics of the electron's anomalous magnetic moment $a_e$ in nonperturbative QED, and (2) the practical problems of ultraviolet regularization and renormalization in truncated nonperturbative light-cone Hamiltonian theory. We present results for $a_e$ computed in a light-cone gauge Fock space truncated to include one bare electron and at most two photons; i.e., up to two photons in flight. The calculational scheme uses an invariant mass cutoff, discretized light-cone quantization (DLCQ), a Tamm--Dancoff truncation of the Fock space, and a photon mass regulator. We introduce new weighting methods which greatly improve convergence to the continuum within DLCQ. Nonperturbative renormalization of the coupling and electron mass are carried out, and a limit on the magnitude of the effective physical coupling strength is computed. A large renormalized coupling strength $\alpha_R= 0.1$ is then used to make the nonperturbative effects in the electron anomalous moment from the one-electron, two-photon Fock state sector numerically detectable.