H. Sonoda Physics Department, Kobe University, Kobe 657-8501, Japan (Dated: September 1, 2020) 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.

中文翻译：

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精确重整化群形式主义中当前算子的乘积

H. Sonoda 物理系，神户大学，神户 657-8501，日本（日期：2020 年 9 月 1 日） 摘要 给定全局手性变换下的威尔逊作用不变量，我们可以根据威尔逊作用构造当前复合算子。当前算子的多个乘积中的短距离奇点由精确重整化群处理。Ward-Takahashi 恒等式与威尔逊作用的有限动量截断兼容。精确重整化群和 Ward-Takahashi 恒等式共同决定了乘积。作为一个具体的例子，我们研究了手性费米子的高斯不动点威尔逊作用来构造当前算子的乘积。