Axial anomaly: the modern status

Abstract

The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: 1) by splitting of coordinates in the expression for the axial current and 2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advantages in the case of description of the anomaly by contribution of hadronic states in QCD. The validity of the t'Hooft consistency condition is discussed. Few examples of the physical application of the axial anomaly are given.

17 pages, 3 figures, to be published in International Journal of Modern Physics A, few minor correction were done, two references were added

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• Reconnection of magnetic fields in neutron stars driven by the electron mass term in the triangle anomaly
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• Chiral anomaly in inhomogeneous systems with nontrivial momentum space topology
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