从幺正性和解析性考察量子场论的红外发散

Investigations of Infrared Divergence in Quantum Field Theory from Unitarities and Analyticities

本文从S矩阵幺正性和解析性要求的角度,考察了量子场论中红外发散问题。指出QED范围内在α的任何阶,任一泡泡图虛部的红外发散应该在此泡泡图按Landau-Cutkosky规则得出的切割泡泡图小集内相互对消。其次从散射振幅解析性的基本假定和广义光学定理概念出发,对"弹性朝前散射"幺正性的普遍表达式引伸出有物理实际的内涵,并得出QED中判断某过程存在红外发散与否的一般准则。最后再以π(q^2)的泡泡图在q^2平面上解析性随光子质量λ的变化,图示性地说明其中红外发散是如何对消的。此外简短最后讨论了推广到QCD时的困难和问题。

In this paper we have investigated the infrared divergence in QFT from the point of view of unitarities and analyticities. We have shown that in QED, the infrared divergence for the imaginary part of a bubble diagram at any order of α would be canceled each other between the set of cutting-bubble diagrams got from cutting rules of Landau Cutkosky. From the concept of generalized optical theorem and the hypothesis of analyticities of the scattering amplitude, we have drawn the physical connotation from the general formula of unitarity, for 'forward scattering processes', and thus getting a criterion in QED for whether in a process there exist infrared divergence or not. Also from the variation of thresholds of a bubble diagram of π(q^2) in the—q^2 plane as the photon mass λ approaches to zero, we have shown diagrammatically how the infrared divergence in the corresponding cutting-bubble diagrams be canceled between them. At last we give a short discussion about difficulties and problems for treating infrared divergence in QCD.