Abstract
Abstract 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.
Highlights
It is a principle of quantum field theory that the invariance of a theory under a continuous transformation implies the conservation of a current
When a theory is expressed by a Wilson action with a finite momentum cutoff, the principle holds for the Wilson action
Well defined exact renormalization group (ERG) differential equations admit only the solutions consistent with locality, i.e., the vertices of the action and composite operators must be analytic at zero momenta
Summary
It is a principle of quantum field theory that the invariance of a theory under a continuous transformation implies the conservation of a current. In this paper we would like to consider the Wilson action of chiral fermions with global flavor symmetry to construct multiple products of the conserved current operator. (See for example [2,3,4,5] and references therein.) The Wilson action satisfies a well defined differential equation under the continuous change of scale. Well defined ERG differential equations admit only the solutions consistent with locality, i.e., the vertices of the action and composite operators must be analytic at zero momenta. This is the guiding principle we follow throughout the paper.
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