论文标题
$ r^*$ - 操作的Hopf代数结构
The Hopf algebra structure of the $R^*$-operation
论文作者
论文摘要
我们给出了$ r^*$ - 操作的Hopf-elgebraic公式，这是渲染UV和IR发散欧几里得Feynman图有限的规范方法。我们的分析发现了与Motic图的Brown的Hopf代数的密切联系。使用这种连接，我们能够提供紫外线和IR减法的长期观察到的详细证明。我们还给出了紫外线和IR对抗之间的新二元性，本质上完全代数为代数，作为对log-Dim-Dim-Dim-Dim-Dim-Dim-Dim-Diover无尺度无限制Feynman图的字符组的反相关关系。给出了许多与红外重排应用的计算示例。
We give a Hopf-algebraic formulation of the $R^*$-operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close connection to Brown's Hopf algebra of motic graphs. Using this connection we are able to provide a verbose proof of the long observed 'commutativity' of UV and IR subtractions. We also give a new duality between UV and IR counterterms, which, entirely algebraic in nature, is formulated as an inverse relation on the group of characters of the Hopf algebra of log-divergent scaleless Feynman graphs. Many explicit examples of calculations with applications to infrared rearrangement are given.
