Treatment of closed fermion loops in quantum electrodynamics

A careful treatment of closed fermion loops in quantum electrodynamics is developed starting from Schwinger's gauge invariant formulation of the current, involving a line integral, in an external field problem. The analysis is carried out for multiloop contributions and to all orders of perturbation theory. The derived vanishing property of closed fermion loops when any subset of the external photon momenta is set equal to zero has a very important role in the renormalization program as this does not necessitate the introduction of the unwanted light-light scattering contact term in the Lagrangian. This also permits taking the limit of the photon zero-mass at least for Euclidean nonexceptional external momenta. The functional approach, used in this work, is found to be particularly suited for treating the closed fermion loop problem. 10 refs. (author)