Anomaly (physics)
Categories: Quantum field theory
In physics, an anomaly is a classical symmetry — a symmetry of the Lagrangian — that is broken in quantum field theories.
Any anomaly can be considered to be a short-distance effect (an ultraviolet effect, in the language of quantum field theory), since it arises during the process of renormalization, when some divergent integrals cannot be regularized in such a way that all the symmetries are preserved simultaneously. However, their effects are often felt at long distances (ie, by the infra-red physics, in the language of quantum field theory) since the lack of this classical symmetry is often manifested in the physics of massless (or nearly massless) particles described by the theory.
Anomalies in global symmetries pose no problems in a quantum field theory, and are often encountered (see the example of the chiral anomaly). Anomalies in gauge theories pose problems, since a gauge symmetry is usually required by the phenomenon under study. The attempt to remove them, ie, to build theories consistent with the gauge symmetries often leads to extra constraints on the theories (such is the case of the gauge anomaly in the standard model of particle physics). Anomalies in gauge theories have important connections to the topology and geometry of the gauge group.
Examples
- consistent anomaly
- covariant anomaly
- conformal anomaly
- chiral anomaly
- gravitational anomaly
- gauge anomaly
- mixed anomaly
- global anomaly
- parity anomaly
- diffeomorphism anomaly
Anomaly cancelation
note that all the anomaly cancellation mechanisms result in a spontaneous symmetry breaking of the symmetry whose anomaly is being cancelled.
| Quantum field theory |
| Field theory - overview of QFT - gauge theory - quantization - renormalization - partition function - vacuum state - anomaly - spontaneous symmetry breaking - condensates
Some models: standard model - quantum electrodynamics - quantum chromodynamics Related topics: quantum mechanics - Poincare symmetry |