Light cone formulation of two-dimensional Q.E.D

Starting from an explicit operator solution to Schwinger's 2-dimensional Q.E.D. we investigate the problems which arise in formulating this theory on the light cone. Taking proper care of the independent variables and quantizing the theory with the help of Schwinger's action principle, a consistent solution is presented with initial data given on lightlike surfaces. It is shown how the usual spacelike recipe for the current is to be carried over in a light-cone formulation. The Wightman and Green's functions and their regularization on the light cone is discussed. The charge distribution of the fermion field is investigated