Products of current operators in the exact renormalization group formalism

Given a Wilson action invariant under global chiral transformations, we can construct current composite operators in terms of the Wilson action. The short-distance singularities in the multiple products of the current operators are taken care of by the exact renormalization group. The Ward-Takahashi identity is compatible with the finite momentum cutoff of the Wilson action. The exact renormalization group and the Ward-Takahashi identity together determine the products. As a concrete example, we study the Gaussian fixed-point Wilson action of the chiral fermions to construct the products of current operators.