We revisit the implications of Haag's theorem in the light of the renormalization group. There is still some lack of discussion in the literature about the possible impact of the theorem on the standard (as opposite of axiomatic) quantum field theory, and we try to shed light in this direction. Our discussion then deals with the interplay between Haag's theorem and renormalization. While we clarify how perturbative renormalization (for the sub-class of interactions that are renormalizable) marginalizes the its impact when the coupling is formally small, we argue that a non-perturbative and non-ambiguous renormalization cannot be built if there is any reference to the interaction picture with free fields. In other words, Haag's theorem should be regarded as a no-go theorem for the existence of a non-ambiguous analytic continuation from perturbative to non-perturbative QFT.
Renormalization Ambiguities in Chern-Simons Theory
我们引入了一个新的Chern-Simons理论的规范不变正则化的家庭，产生的形式$k\to k+2 s c_v$，其中$s$可以采取任何任意整数值的耦合常数的单圈重整化。在特定的情况下，$s=0$，我们得到一个明确的例子规范不变正则化，不产生辐射修正裸耦合常数。对$k$辐射修正的这种模糊性使人想起Coste-Lüscher对（2+1）费米子有效作用量宇称反常的结果。
PMC$_\infty$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD
Fixing the Renormalization of Inflationary Loops via Ward Identities
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础科学与数学学院）
Renormalized new solutions for the massless Thirring model
本文用路径积分方法对（1+1）维无质量Thirring模型进行了非微扰研究。正则化的模糊性-来自费米子行列式的计算-允许为模型找到新的解决方案类型。在量子水平上的1 PI 2-点函数的费米电流的沃德恒等式分离这样的解决方案在两个阶段或部门，第一个有一个本地规范对称性，这是在量子水平上实现的，而另一个没有这种对称性。对称阶段是一个新的解决方案，这是无关的模型的以前的研究，并在非对称阶段，有解决方案，对于某些值的模糊度参数是相关的模型的众所周知的解决方案。我们构造了Schwinger-Dyson方程和沃德恒等式。我们对它们的紫外发散结构进行了详细的分析，然后对模型进行了非微扰正则化和重正化。
