Anomaly (physics)

<p>In <a href="/facts/Quantum_physics/BRc3Mzgr">quantum physics</a> an anomaly or quantum anomaly is the failure of a <a href="/facts/Symmetry/hpu7DK8p">symmetry</a> of a theory's classical <a href="/facts/Action_(physics)/NhWS2Mts">action</a> to be a symmetry of any <a href="/facts/Regularization_(physics)/mzFLfUgl">regularization</a> of the full quantum theory.  
In <a href="/facts/Classical_physics/gGnINVPE">classical physics</a>, a classical anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking parameter goes to zero. Perhaps the first known anomaly was the dissipative anomaly in <a href="/facts/Turbulence/NpgFUhG5">turbulence</a>: time-reversibility remains broken (and energy dissipation rate finite) at the limit of vanishing <a href="/facts/Viscosity/QLVfrdCz">viscosity</a>. 
</p><p>In quantum theory, the first anomaly discovered was the <a href="/facts/Adler%25E2%2580%2593Bell%25E2%2580%2593Jackiw_anomaly/xs7QFslR">Adler–Bell–Jackiw anomaly</a>, wherein the <a href="/facts/Chiral_anomaly/xs7QFslR">axial vector current</a> is conserved as a classical symmetry of <a href="/facts/Electrodynamics/oAkmALHT">electrodynamics</a>, but is broken by the quantized theory. The relationship of this anomaly to the <a href="/facts/Atiyah%25E2%2580%2593Singer_index_theorem/qwcSxamI">Atiyah–Singer index theorem</a> was one of the celebrated achievements of the theory. Technically, an anomalous symmetry in a quantum theory is a symmetry of the <a href="/facts/Action_(physics)/NhWS2Mts">action</a>, but not of the measure, and so not of the <a href="/facts/Partition_function_(quantum_field_theory)/T6VtrIo6">partition function</a> as a whole.
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Anomaly (physics) open-in-new

Anomaly (physics)