The photon propagator is analyzed by means of general properties of the present theory of electrons and photons. It can be shown, by consideration of the charge renormalization group, that the photon propagator is independent of physical charge in the high energy limit. If, in addition to renormalizability, regularity at vanishing physical charge is assumed, then it follows that the bare charge vanishes. On the other hand, the commonly assumed analyticity properties require that bare charge exceeds physical charge. Thus at least one of the general properties assumed is inadmissible. This relationship of expressions satisfying the charge renormalization group equations to analyticity properties and definite sets of Feynman diagrams (which correspond to an expansion about zero charge) is illustrated by a simple example.