Discretized light-cone quantization: The massless and the massive Schwinger model

The method of discretized light-cone quantization (DLCQ), recently proposed for obtaining nonperturbative solutions to field theories, is applied to quantum electrodynamics in one space dimension (${\mathrm{QED}}_2$). The spectrum of invariant masses and the eigenfunctions of the light-cone Hamiltonian are calculated; i.e., the bound-state problem is solved for all values of the coupling constant. For very strong coupling (Schwinger model proper) DLCQ reproduces one to one the known exact solutions. For nonvanishing fermion mass (massive Schwinger model) the results of DLCQ agree with earlier work and in particular with a lattice gauge calculation.