Quantizing QED2 on the light-cone

The method of discretized light-cone quantization (DLCQ) is applied to quantum electrodynamics in one space and one time dimension (QED₂) with different initial conditions. This leads to different representations of the operators of the constants of motion. Within the fermion-antifermion approximation we perform analytically the transition to the continuum limit and show that the discrete massive and massless representations are equivalent. We compare a semiclassical calculation of the number of bound states with the results obtained in the continuum limit. Furthermore a discrete bosonized version of QED₂ is discussed.