Editing Anomaly (physics) (section)

==At different energy scales==

{{Main article|Anomaly matching condition}}

Quantum anomalies were discovered via the process of [[renormalization]], when some [[ultraviolet divergence|divergent integrals]] cannot be [[regularization (physics)|regularized]] in such a way that all the symmetries are preserved simultaneously. This is related to the high energy physics. However, due to [[Gerard 't Hooft]]'s [[anomaly matching condition]], any [[chiral anomaly]] can be described either by the UV degrees of freedom (those relevant at high energies) or by the IR degrees of freedom (those relevant at low energies). Thus one cannot cancel an anomaly by a [[UV completion]] of a theory—an anomalous symmetry is simply not a symmetry of a theory, even though classically it appears to be.