  We give a functional derivation of the Ward-Takahashi identity for Yang-Mills
theory in the framework of the exact renormalization group. The identity
realizes non-abelian gauge symmetry nontrivially despite the presence of a
momentum cutoff. The cutoff deforms the gauge transformation by introducing
composite operators. In our functional method, which is an extension of the
method used in our previous work on QED, these composite operators are
expressed in terms of the Wilson action that depends on both a UV cutoff and an
IR cutoff.
