Anomalies, Unitarity, and Quantum Irreversibility
Anomalies, Unitarity, and Quantum Irreversibility
复制标题
反常、幺正性和量子不可逆性
DOI：
10.1006/aphy.1999.5949
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发表时间：
1999
影响因子：
3
通讯作者：
D. Anselmi
中科院分区：
文献类型：
--
作者：
D. Anselmi
摘要 外部重力的迹异常是临界点三项的总和：Weyl 张量的平方、欧拉密度和 □R，其系数经过适当归一化，称为 c、a 和 a′，后者由加性常数模糊定义。关于诱导动作的幺正性和正性性质的考虑使我们能够证明 a 和 a' 的总 RG 流是相等的，因此可以通过识别 a'=a 一致地消除 a' 模糊性。出现的情况澄清了几个长期存在的问题。酉性和重整化之间的相互作用意味着重整化群的通量是不可逆的。 a' 自然地提供了在适当值之间插值的单调递减 a 函数。总 a 流以非扰动方式表示为固定点之间 beta 函数图的不变（即与方案无关）面积。我们在微扰理论、Nf≲11/2Nc 的 QCD 和超对称 QCD 中测试了这一预测的第四循环阶。在不存在相互作用不动点的情况下也达成了一致（QED 和 phi4 理论）。还讨论了 a 的积极性的论证。
Abstract The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and □R, with coefficients, properly normalized, called c, a, and a′, the latter being ambiguously defined by an additive constant. Considerations about unitarity and positivity properties of the induced actions allow us to show that the total RG flows of a and a′ are equal and therefore the a′-ambiguity can be consistently removed through the identification a′=a. The picture that emerges clarifies several long-standing issues. The interplay between unitarity and renormalization implies that the flux of the renormalization group is irreversible. A monotonically decreasing a-function interpolating between the appropriate values is naturally provided by a′. The total a-flow is expressed non-perturbatively as the invariant (i.e., scheme-independent) area of the graph of the beta function between the fixed points. We test this prediction to the fourth loop order in perturbation theory, in QCD with Nf≲11/2Nc and in supersymmetric QCD. There is agreement also in the absence of an interacting fixed point (QED and ϕ4-theory). Arguments for the positivity of a are also discussed.