Adel Bilal developed a detailed field-theoretic account of quantum anomalies. His lectures derive the chiral anomaly through changes of the functional measure and triangle diagrams, then relate gauge anomalies to nonconservation and consistency conditions.[ref]
Lectures on Anomalies by Adel Bilal. Abstract and anomaly derivations, consistency conditions and cancellation
An anomaly is not simply an inaccurate approximation: a symmetry of the classical description may fail after quantization. In a gauge theory, the relevant cancellation conditions constrain the allowed particle representations. This connects explicit diagram calculations with structural restrictions on a quantum field theory.
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