Symmetry and combinatorics in the expansion for QED

Combinatorics and symmetry are used to solve calculational problems in applying the -expansion method to QED. Adequate Feynman rules are used to simplify previous calculations and Ward identities are obtained. In the case with no external fermions an equivalence to the conventional loop expansion is established, both through the use of path integrals and through explicit calculations of the effective vertices. The Ward identities are reduced in this case to the conventional ones implied by gauge invariance.