发表机构
Universite de Lorraine（洛林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了微扰重整化的Polchinski流与Connes-Kreimer方法等价，通过带装饰图的假设和组合重整化求解Polchinski方程，推导出文献中最一般的重整化势形式。
AI 中文摘要
我们证明了微扰重整化的Polchinski流方法与Connes-Kreimer方法之间存在对应关系，即前者产生的重整化结果与后者相同。更确切地说，我们表明基于带装饰图（费曼图）的假设，结合组合重整化过程可以求解Polchinski方程，该结果适用于非常一般的欧几里得量子场论。我们由此能够推导出重整化势的形式，据我们所知，这是文献中最一般的形式。证明的主要要素是关于重整化的多重态性质，以及带装饰图的森林的新对偶公式。
英文摘要
We prove a correspondence between the Polchinski flow and the Connes-Kreimer approaches to perturbative renormalisation, in the sense that the first yields the same renormalisation as the latter. More precisely, we show that an ansatz based on decorated graphs (Feynman diagrams),with a combinatorial renormalisation procedure solves the Polchinski equation. This result holds for very general Euclidean quantum field theories. We are able to derive from this the form of the renormalised potential which is, to the best of our knowledge, the most general one in the literature. The main ingredients of the proof are multiple morphism properties with respect to the renormalisation, as well as a novel duality formula for forests of decorated graphs.
Comments29 pages
