论文标题
差异不变性需要共形异常
Diffeomorphism Invariance Demands Conformal Anomalies
论文作者
论文摘要
我们研究了一系列通过反复整合在较高环上出现的保形因子场的共形异常来获得的WESS-Zumino作用。我们表明它们是作为使非局部环校正项差异不变所需的物理量出现的。具体而言，在一个固定平坦的时空$ ds^2 = e^{2 ϕ}（-dη^2 + d {\ bf x}^2）$中，我们发现有效的动作描述了有效的动作以物理$ q^2 = q^2 = q^2 = q^2/e^2/e^2/e^{2 ϕ $ q^2 $ q^2 $ quarts forthy Mongum and the Mongorm and the Mongorm of the Mongum shomps of the Mongum nossum nevers the Mongum nosem nevers of n homents，这在宇宙学。通过使用维尺寸正则化来计算在3循环水平的曲线时段中QED的有效作用来证实。 QCD的情况也是如此，我们在其中表明，可以以物理动量描述的运行耦合常数平方平方的倒数形式总结有效的动作。我们还看到，对于可恢复的量子保质重力也有同样的态度，并且保形异常对于制定理论是必不可少的。
We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make nonlocal loop correction terms diffeomorphism invariant. Specifically, in a conformally flat spacetime $ds^2=e^{2ϕ}(-dη^2 + d{\bf x}^2)$, we find that effective actions are described in terms of momentum squared expressed as a physical $Q^2 = q^2/e^{2ϕ}$ for $q^2$ measured by the flat metric, which recalls the relationship between physical momentum and comoving momentum in cosmology. It is confirmed by calculating the effective action of QED in such a curved spacetime at the 3-loop level using dimensional regularization. The same applies to the case of QCD, in which we show that the effective action can be summarized in the form of the reciprocal of a running coupling constant squared described by the physical momentum. We also see that the same holds for renormalizable quantum conformal gravity and that conformal anomalies are indispensable for formulating the theory.
