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第358行： − 在完全共形对称条件下，尺度不变量子图几乎都是不变的，对此类量子图的研究是共形场论的。CFT 中的算子有一个定义良好的尺度维度，类似于上面讨论的经典场的尺度维度 something。然而，CFT 中算子的尺度维数与经典理论中场的尺度维数不同。在 CFT 中出现的附加贡献被称为异常尺度维数。+ − +
→Conformal field theory 共形场论
Scale-invariant QFTs are almost always invariant under the full conformal symmetry, and the study of such QFTs is conformal field theory (CFT). Operators in a CFT have a well-defined scaling dimension, analogous to the scaling dimension, ∆, of a classical field discussed above. However, the scaling dimensions of operators in a CFT typically differ from those of the fields in the corresponding classical theory. The additional contributions appearing in the CFT are known as anomalous scaling dimensions.
Scale-invariant QFTs are almost always invariant under the full conformal symmetry, and the study of such QFTs is conformal field theory (CFT). Operators in a CFT have a well-defined scaling dimension, analogous to the scaling dimension, ∆, of a classical field discussed above. However, the scaling dimensions of operators in a CFT typically differ from those of the fields in the corresponding classical theory. The additional contributions appearing in the CFT are known as anomalous scaling dimensions.
在完全共形对称条件下，标度不变的量子场论几乎总是不变的，对此类量子场论的研究就是共形场论（CFT）。共形场论中的算子具有定义明确的标度维数，类似于前面所讨论的经典场标度维数 ''∆''。然而，共形场论中算子的标度维数与经典理论中场的标度维数不同。在共形场论中出现的附加贡献称做'''Anomalous Scaling Dimensions 异常标度维数'''。
===Scale and conformal anomalies 标度与共性异常===
===Scale and conformal anomalies 标度与共形异常===
The φ<sup>4</sup> theory example above demonstrates that the coupling parameters of a quantum field theory can be scale-dependent even if the corresponding classical field theory is scale-invariant (or conformally invariant). If this is the case, the classical scale (or conformal) invariance is said to be [[conformal anomaly|anomalous]]. A classically scale invariant field theory, where scale invariance is broken by quantum effects, provides an explication of the nearly exponential expansion of the early universe called [[Inflation (cosmology)|cosmic inflation]], as long as the theory can be studied through [[perturbation theory]].<ref>{{cite journal|last=Salvio, Strumia|title=Agravity|journal=JHEP |volume=2014 |issue=6|pages=080|date=2014-03-17|url=http://inspirehep.net/record/1286134|arxiv = 1403.4226|bibcode = 2014JHEP...06..080S|doi=10.1007/JHEP06(2014)080}}</ref>
The φ<sup>4</sup> theory example above demonstrates that the coupling parameters of a quantum field theory can be scale-dependent even if the corresponding classical field theory is scale-invariant (or conformally invariant). If this is the case, the classical scale (or conformal) invariance is said to be [[conformal anomaly|anomalous]]. A classically scale invariant field theory, where scale invariance is broken by quantum effects, provides an explication of the nearly exponential expansion of the early universe called [[Inflation (cosmology)|cosmic inflation]], as long as the theory can be studied through [[perturbation theory]].<ref>{{cite journal|last=Salvio, Strumia|title=Agravity|journal=JHEP |volume=2014 |issue=6|pages=080|date=2014-03-17|url=http://inspirehep.net/record/1286134|arxiv = 1403.4226|bibcode = 2014JHEP...06..080S|doi=10.1007/JHEP06(2014)080}}</ref>