Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 305 / 2 / a / Solution

A quantum anomaly occurs when a symmetry of the classical action cannot be preserved by the regulator or functional measure of the quantum theory. An anomaly in a global symmetry is physically allowed: it changes a classical current conservation law and can mediate observable processes. A gauge anomaly is fatal unless it cancels, because gauge symmetry is the redundancy that removes negative-norm and longitudinal unphysical states; its loss spoils the gauge Ward identities and unitarity.