arXiv 2210.161832022-10-03hep-phhep-th

非阿贝尔规范理论中的红外发散和低能定理

Infrared Divergence and Low Energy Theorem in Non-Abelian Gauge Theory

Akio Sugamoto

备注：: 76 pages, 132 figures. The English translation of the Doctor thesis submitted to the University of Tokyo in March 1978. Its Japanese version was published in Soryushiron Kenkyu 60-2 (1979-11) pp. 47-117. An appendix is newly added, which is the excerption of a relevant mathematical part of a report submitted to Prof. Mikio Sato in August 1976.

摘要：

在本论文中，首先回顾了QED中红外发散角的消除。接下来，在QCD中的两个例子，夸克-夸克散射和夸克-胶子散射检查在一个循环，从Ward-Takahashi恒等式的重要性变得明显的取消发生。利用Ward-Takahashi恒等式，证明了QCD中红外发散的全阶因式分解。在这些证明中，使用了轴向规范条件。量子色动力学中红外发散的抵消发生在规范不变的图形集合中。这样，F. E.低，发射一个或两个软胶子，证明在所有的订单。由此导出了控制QCD中红外发散的微分方程。在QCD中，耦合常数重整化引入了另一种红外发散，这种发散在纯Yang-Mills理论中由β函数控制。在2022年的后记中，简要说明了最近将论文翻译成英语的动机。

英文摘要：

In the thesis, first, the cancellation of infrared divergences in QED is reviewed. Next, two examples in QCD, the quark-quark scattering and the quark-gluon scattering are examined at one loop, from which the importance of Ward-Takahashi identities becomes manifest for the cancellation to occur. The factorization of infrared divergences in QCD is proved at all orders, by full usage of the Ward-Takahashi identities. In these proofs, the axial gauge condition is used. The cancellation of infrared divergences in QCD occurs among the gauge invariant set of graphs. In this way, the low energy theorem of F. E. Low, for emission of one or two soft gluons, are proved at all orders. From this, the differential equation controlling the infrared divergences in QCD is derived. In QCD, the coupling constant renormalization introduces the other infrared divergence, which is governed by the beta-function in the pure Yang-Mills theory. In the Epilogue 2022, a motivation for recently translating the thesis in English is briefly stated.

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摘要：

英文摘要：

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