$\gamma_{5}$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$

Understand

We address the subject of chiral anomalies in two and four dimensional theories.

• Ambiguities associated with the $\gamma_5$ 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.