Light-Cone Quantization of the Schwinger Model

We consider constructing a canonical quantum theory of the light-cone gauge ($A_{-}$=0) Schwinger model in the light-cone representation. Quantization conditions are obtained by requiring that translational generators $P_{+}$ and $P_{-}$ give rise to Heisenberg equations which, in a physical subspace, are consistant with the field equations. A consistent operator solution with residual gauge degrees of freedom is obtained by solving initial value problems on the light-cones. The construction allows a parton picture although we have a physical vacuum with nontrivial degeneracies in the theory.