费曼振幅中的$γ_{5}$代数二义性：$D=4$和$D=2$中的动量路由不变性和反常
$γ_{5}$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$
摘要：
我们讨论二维和四维理论中的手征反常问题。与$γ_5$代数内的发散积分的歧义被识别，即使在正则化的过程中的物理尺寸没有改变。我们提出了一个最小的处方，导致独特的结果，并将其应用到一系列的例子。对于具有有效手征顶点的阿贝尔理论的特殊情况，我们证明了：1-它对民主地显示沃德恒等式中的反常的方法的意义。2-以这样一种方式固定任意表面项的可能性，即出现与动量路由无关的结果。这导致重新解释的作用，动量路由的过程中选择的沃德恒等式，以满足在一个异常的过程。3-动量路由不变性（MRI）是保证有效手征阿贝尔规范理论矢量规范不变性的充分必要条件。我们还简要地讨论了完整的手征理论的情况下，使用手征Schwinger模型作为一个例子。
英文摘要：
We address the subject of chiral anomalies in two and four dimensional theories. Ambiguities associated with the $γ_5$ algebra within divergent integrals are identified, even though the physical dimension is not altered in the process of regularization. We present a minimal prescription that leads to unique results and apply it to a series of examples. For the particular case of abelian theories with effective chiral vertices, we show: 1- Its implication on the way to display the anomalies democratically in the Ward identities. 2- The possibility to fix an arbitrary surface term in such a way that a momentum routing independent result emerges. This leads to a reinterpretation of the role of momentum routing in the process of choosing the Ward identity to be satisfied in an anomalous process. 3- Momentum Routing Invariance (MRI) is a necessary and sufficient condition to assure vectorial gauge invariance of effective chiral Abelian gauge theories. We also briefly discuss the case of complete chiral theories, using the Chiral Schwinger Model as an example.
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