Editing Mixed anomaly

{{short description|Gauge anomaly from multiple gauge groups}}
In [[theoretical physics]], a '''mixed anomaly''' is an example of an [[anomaly (physics)|anomaly]]: it is an effect of [[quantum mechanics]] — usually a [[one-loop diagram]] — that implies that the classically valid [[general covariance]] and [[gauge symmetry]] of a theory of [[general relativity]] combined with [[gauge field]]s and [[fermion]]ic fields cannot be preserved simultaneously in the quantum theory.

The adjective "mixed" usually refers to a mixture of a [[gravitational anomaly]] and [[gauge anomaly]], but may also refer to a mixture of two different gauge groups tensored together, like the ''SU(2)'' and the ''U(1)'' of the [[Standard Model]].

The anomaly usually appears as a [[Feynman diagram]] with a [[chirality (physics)|chiral]] [[fermion]] running in the loop (a polygon) with ''n−k'' external [[graviton]]s and ''k'' external [[gauge boson]]s attached to the loop where <math>n=1+D/2</math> where <math>D</math> is the [[spacetime]] dimension. Chiral fermions only occur in even spacetime dimensions. For example, the anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams.

[[Image:Triangle diagram.svg]]

General covariance and gauge symmetries are very important symmetries for the [[consistency]] of the whole theory, and therefore all gravitational, gauge, and mixed anomalies must cancel out.

==References==
* {{cite book
 |last1=Cheng |first1=T.P.|last2=Li |first2=L.F. |date=1984 |title=Gauge Theory of Elementary Particle Physics|publisher=Oxford Science Publications }}   

== See also ==

* [[Gravitational anomaly]]
* [[Green–Schwarz mechanism]]

{{quantum gravity}}

{{DEFAULTSORT:Mixed Anomaly}}
[[Category:Anomalies (physics)]]
[[Category:Quantum gravity]]


{{Quantum-stub}}