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A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric (Weyl transformations), combined with corresponding transformations of the other fields in the theory. A conformal quantum theory is one whose partition function is unchanged by rescaling the metric. The variation of the action with respect to the background metric is proportional to the stress tensor, and therefore the variation with respect to a conformal rescaling is proportional to the trace of the stress tensor. As a result, the trace of th

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rdfs:label	Conformal anomaly (en) Anomalia conforme (pt) 共形反常 (zh)
rdfs:comment	A anomalia conforme, anomalia de escala, ou anomalia de Weyl é uma anomalia, ou seja, um fenômeno quântico que quebra a simetria conformal da teoria clássica. (pt) 共形反常是一種在量子化過程中出現的一個現象。以愛因斯坦場方程式的能動張量為例，當有效作用量經由重整化後，會產生一個正的量值和負的量值，其中物質能動張量的跡不為零，然而重整化前原本的量為零，這意味著原本的對稱關係被破壞，違反共形不變性，即為共形反常。共形反常在重整化後才物理意義，而引起物質能動張量反常的原因則為背景時空的非平直性。 (zh) A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric (Weyl transformations), combined with corresponding transformations of the other fields in the theory. A conformal quantum theory is one whose partition function is unchanged by rescaling the metric. The variation of the action with respect to the background metric is proportional to the stress tensor, and therefore the variation with respect to a conformal rescaling is proportional to the trace of the stress tensor. As a result, the trace of th (en)
dcterms:subject	Anomalies (physics) Quantum chromodynamics String theory Conformal field theory Renormalization group
Wikipage page ID	1931704 (xsd:integer)
Wikipage revision ID	1099558142 (xsd:integer)
Link from a Wikipage to another Wikipage	Quark Anomaly (physics) Anomalies (physics) Joseph Polchinski Virial theorem Pseudoscalar meson Quantum chromodynamics String theory Colour confinement Conformal symmetry Mass Classical field theory Classical theory Conformal field theory Critical dimension Stress–energy tensor String theory Partition function (quantum field theory) Conformal field theory Central charge Dimensional transmutation Quantum chromodynamics Hadron Renormalization group Charge (physics) Chirality (physics) Dimensionality Bosonic string theory Spacetime Matter Vacuum expectation value Weyl transformation Non-critical string theory String (physics) Superstring theory Anomalous scaling dimension Weyl symmetry
sameAs	Conformal anomaly Conformal anomaly Conformal anomaly Conformal anomaly Conformal anomaly Conformal anomaly
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:ISBN dbt:Reflist dbt:Short_description dbt:String_theory_topics
has abstract	A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric (Weyl transformations), combined with corresponding transformations of the other fields in the theory. A conformal quantum theory is one whose partition function is unchanged by rescaling the metric. The variation of the action with respect to the background metric is proportional to the stress tensor, and therefore the variation with respect to a conformal rescaling is proportional to the trace of the stress tensor. As a result, the trace of the stress tensor must vanish for a conformally invariant theory. In the presence of a conformal anomaly the trace of the stress tensor can nevertheless acquire a non-vanishing expectation. For this reason, a conformal anomaly is sometimes also called a trace anomaly. (en) A anomalia conforme, anomalia de escala, ou anomalia de Weyl é uma anomalia, ou seja, um fenômeno quântico que quebra a simetria conformal da teoria clássica. (pt) 共形反常是一種在量子化過程中出現的一個現象。以愛因斯坦場方程式的能動張量為例，當有效作用量經由重整化後，會產生一個正的量值和負的量值，其中物質能動張量的跡不為零，然而重整化前原本的量為零，這意味著原本的對稱關係被破壞，違反共形不變性，即為共形反常。共形反常在重整化後才物理意義，而引起物質能動張量反常的原因則為背景時空的非平直性。 (zh)
prov:wasDerivedFrom	wikipedia-en:Conformal_anomaly?oldid=1099558142&ns=0
page length (characters) of wiki page	5860 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Conformal_anomaly
is Link from a Wikipage to another Wikipage of	Scale invariance Beta function (physics) Anomaly (physics) Index of physics articles (C) Coupling constant Anomaly Stanley Deser Conformal field theory Critical dimension Central charge Dimensional transmutation RST model Charge (physics) Chiral symmetry breaking Coleman–Weinberg potential Bosonic string theory CGHS model List of string theory topics List of things named after Hermann Weyl Scale anomaly Weyl transformation Weyl anomaly
is Wikipage redirect of	Scale anomaly Weyl anomaly
is Wikipage disambiguates of	Anomaly

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