Anomaly (physics)

Under an anomaly in quantum field theory is defined as the breaking of a classical symmetry of a field theory ( in the classical level ) through the process of quantization.

Technically they arise anomalous symmetries, namely by the action functional of the field theory, ie the Lagrangian of the theory, but not required in the quantization measurement functions, and thus is not the so-called generating functional of the theory of symmetry obey ( is the reduced Planck constant, the exponential function ).

The physical relevance of such anomalies manifested, inter alia by the fact that they make a significant contribution to the decays of the neutral pion, respectively, and that in connection with the famous triangle diagram. ( That is converted into an electron upon full revolution around the triangle a positron, is an explicit signature of the anomalous behavior. ) Other examples arise in the so-called Ward identities. Here are equations for quantum mechanical amplitudes occur conservation laws in quantized theories in place of ( cease to be valid by the quantization).

From the viewpoint of quantum field theory considers the designation anomaly is actually not used judiciously, because in the classical limit, disappear ( to the conservation laws belonging ) symmetries not, but the effect are terms in this limit simply dominant against everything else.

Another application of the anomalies is adjacent to the pion decay, the explanation of the absence of a ninth Goldstone boson that would otherwise be required by the QCD.

While anomalies of global symmetries are harmless and can be observed as in the example of the decay in nature, would be abnormalities in the so-called gauge symmetries, who are locally destroy the renormalizability of the theory, which is why gauge symmetries for consistency must always be anomaly- free. For the gauge symmetry of the Standard Model, this is ensured by the fact that the anomalous contributions of the various flavors of quarks and leptons cancel out each other, as long as the number of generations in the quark and Leptonsektor is the same.