  In the functional renormalisation group approach to gauge theory, the
Ward-Takahashi identity is modified due to the presence of an infrared cutoff
term. It take the most accessible form for the Wilsonian effective action.
  In the present work we solve these identities, partially, for the Wilson
effective action of QED. In particular, we compute the longitudinal part of the
photon two point vertex function as a momentum- dependent function in the
presence of the cutoff k. The resultant Wilsonian effective action carries form
factors that originate from the modified Ward-Takahashi identity. We show how
this result carries over to the one-particle-irreducible effective action.
