On the convergence of planar diagram expansions
On the convergence of planar diagram expansions
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关于平面图展开式的收敛性
DOI：
10.1007/bf01214881
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发表时间：
1982
影响因子：
2.4
通讯作者：
G. Hooft
中科院分区：
文献类型：
--
作者：
G. Hooft
在四维欧几里德空间中，研究了SU(∞)规范理论等微扰展开式仅用平面费曼图描述的可重整化量子场理论。为了研究扰动序列的渐近性质，人们可能希望首先分离出不包含任何紫外线散度子图的所有平面图。本文证明了这组无限图求和后，在耦合常数的有限收敛半径内收敛。
Renormalizable quantum field theories whose perturbation expansions are described by planar Feynman diagrams only, such as SU(∞) gauge theory, are considered in 4 dimensional Euclidean space. For studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs. In this paper it is proved that this infinite set of diagrams, when summed, converges within a finite radius of convergence for the coupling constant.