Schwinger used an analytic continuation of the effective action to correctly compute the particle production rate per unit volume for quantum electrodynamics in a uniform electric field. However, if one simply evaluates the one-loop expectation value of the current operator using his propagator, the result is zero! We analyse this curious fact from the context of a canonical formalism of operators and states. The explanation turns out to be that Schwinger's propagator is not actually the expectation value of the time-ordered product of field operators in the presence of a time-independent state, although it is of course a Green function. We compute the true propagator in the presence of a state which is empty at x₊ = 0 where x₊≡(x⁰ + x³)/(2)^1/2 is the lightcone evolution parameter. Our result can be generalized to electric fields which depend arbitrarily on x₊.