Hydraulic machinery: Difference between revisions

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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]].
 
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. Anomalies occur only 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.
 
== See also ==
 
* [[gravitational anomaly]]
* [[Green-Schwarz mechanism]]
 
{{quantum gravity}}
 
{{DEFAULTSORT:Mixed Anomaly}}
[[Category:Anomalies in physics]]
[[Category:Quantum gravity]]
 
 
{{Quantum-stub}}

Revision as of 00:01, 16 February 2014

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