  Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi
identity for the Wilson action of QED. We first rederive the identity using a
functional method. The identity makes it possible to realize the gauge symmetry
even in the presence of a momentum cutoff. In the cutoff dependent realization,
the abelian nature of the gauge symmetry is lost, breaking the nilpotency of
the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the
Wilson action by including the antifield contributions. Then, the
Ward-Takahashi identity for the Wilson action is lifted to a quantum master
equation, and the modified BRS transformation regains nilpotency. We also
obtain a flow equation for the extended Wilson action.
