On the summation of Feynman graphs

A functional method to achieve the summation of all Feynman graphs relevant to a particular Field Theory process is suggested, and applied to QED, demonstrating manifestly gauge invariant calculations of the dressed photon propagator in approximations of increasing complexity. These lead in a natural way to the extraction of the leading logarithmic divergences of every perturbative order, and to a demonstration of the possible cancellation of all such divergences in the calculation of the (inverse of the) photon’s wavefunction renormalization constant Z3. ► Functional representations of the sum of all relevant Feynman graphs. ► Radiative corrections to the photon propagator of QED. ► Estimates of sequentially, perturbative higher-orders. ► Contributions to charge renormalization.