In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics - usually a one-loop diagram - that invalidates the gauge symmetry of a quantum field theory i.e. of a gauge theory. Theoretical physics attempts to understand the world by making a model of reality, used for rationalizing, explaining, and predicting physical phenomena through a physical theory. There are three types of theories in physics: mainstream theories, proposed theories and fringe theories. ... In physics, the word anomaly is used to describe a classical symmetry—i. ... Fig. ... In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...
The anomaly usually appears as a Feynman diagram with a chiralfermion running in the loop (a polygon) with n external gauge bosons attached to the loop where n = 1 + D / 2 where D is the spacetime dimension. Anomalies only occur in even spacetime dimensions. For example, the anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams. A Feynman diagram is a bookkeeping device for performing calculations in quantum field theory, invented by American physicist Richard Feynman. ... A phenomenon is said to be chiral if it is not identical to its mirror image (see Chirality (mathematics)). The fundamental laws of physics may be chiral, as the weak charge is not invariant under a reflection unless particles are replaced by their antiparticles as well, and kaon decay appears... Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ... Gauge bosons are bosonic particles which act as carriers of the fundamental forces of Nature. ... World line of the orbit of the Earth depicted as a circle in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, Z, making the circle appear as a helix. ...
triangle feynman diagram File links The following pages link to this file: Chiral anomaly One-loop Feynman diagram Gravitational anomaly Gauge anomaly Mixed anomaly Categories: User-created public domain images ...
Gauge symmetry is a very important symmetry for the consistency of the whole theory, and therefore all gauge anomalies must cancel out.
Historically quantum anomalies have often been considered to be short-distance effects (ultraviolet effects, in the language of quantum field theory), as they arise during the process of renormalization, when some divergent integrals cannot be regularized in such a way that all the symmetries are preserved simultaneously.
In the case of one-loop anomalies, which are the only sources of anomalies of gauge symmetries, one can show that in general anomalies are determined entirely by the quantum numbers of the elementary fields.
Anomalies in gauge theories have important connections to the topology and geometry of the gauge group.
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