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<p>82.157.59.89: /* Composition */ switched two words to past-tense</p> <hr /> <div>[[Image:Triangle_diagram.svg|thumb|right|Anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams]]<br /> {{Distinguish|Gravity anomaly}}<br /> In [[theoretical physics]], a '''gravitational anomaly''' is an example of a [[gauge anomaly]]: it is an effect of [[quantum mechanics]]–usually a [[one-loop diagram]]—that invalidates the [[general covariance]] of a theory of [[general relativity]] combined with some other fields. The adjective &quot;gravitational&quot; is derived from the symmetry of a gravitational theory, namely from general covariance. It is also known as ''diffeomorphism anomaly'', since [[general covariance]] is symmetry under coordinate reparametrization; i.e. [[diffeomorphism]].<br /> <br /> General covariance is the basis of [[general relativity]], the current theory of [[gravitation]]. Moreover, it is necessary for the consistency of any theory of [[quantum gravity]], since it is required in order to cancel unphysical degrees of freedom with a negative norm, namely [[graviton]]s polarized along the time direction. Therefore all gravitational anomalies must cancel out. <br /> <br /> The anomaly usually appears as a [[Feynman diagram]] with a [[chirality (physics)|chiral]] [[fermion]] running in the loop (a polygon) with ''n'' external [[graviton]]s attached to the loop where &lt;math&gt;n=1+D/2&lt;/math&gt; where &lt;math&gt;D&lt;/math&gt; is the [[spacetime]] dimension. Anomalies occur only in even spacetime dimensions. However, anomalies can occur in the case of an odd dimensional spacetime manifold with boundary.<br /> <br /> == See also ==<br /> * For a different concept in [[geodesy]] and [[geophysics]], dealing with differences between observed values of [[gravity]] and predicted values for that location, see [[gravity anomaly]].<br /> * [[mixed anomaly]]<br /> * [[Green-Schwarz mechanism]]<br /> <br /> == References ==<br /> * {{cite journal | last = Alvarez-Gaumé | first = Luis | coauthors = [[Edward Witten]] | title = Gravitational Anomalies | journal = Nucl. Phys. B | volume = 234 | issue = 2 | pages = 269 | date = 1984 | doi = 10.1016/0550-3213(84)90066-X |bibcode = 1984NuPhB.234..269A }}<br /> <br /> {{quantum-stub}}<br /> <br /> {{quantum gravity}}<br /> <br /> [[Category:Anomalies in physics]]<br /> [[Category:Quantum gravity]]</div>

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