A procedure for reducing the functional integral of QED to an integral over
bosonic gauge invariant fields is presented. Next, a certain averaging met
hod for this integral, giving a tractable effective quantum field theory, i
s proposed. Finally, the current-current propagator and the chiral anomaly
are calculated within this new formulation. These results are part of our p
rogramme of analyzing gauge theories with fermions in terms of local gauge
invariants.