ON SINGULARITIES OF AMPLITUDES IN A PERTURBATION THEORY

摘要 本文讨论了二个问题:一、当振幅须对二个以上的外质量进行开拓时,说明了开拓的次序对最后结果有关;二、指出了非朗道奇异点有二种:一种是Cutkosky所指出的,对于这一种,讨论了它与内质量无关的条件,并求出了它对于一圈的费曼图的位置;对于另一种,指出了它的来源,证明了它与内质量无关,并说明了它只对极少数图出现。 Abstract This short paper gives two remarks on the singularities of the scattering amplitudes in a perturbation theory. First, it is pointed out that if the condition of stability is violated at several corners of a Feynmann diagram so that analytic extensions with respect to several external masses must be made, different sequences of carrying out the analytic extensions may lead to different positions of the singularities with respect to the final position of the integration contour (in a dispersion integral) and hence to different expressions for the amplitudes. Next, it is pointed out that the non-Landau singularities fall into two classes, of which one, say the first, is given by Cutkosky. For singularities in the first class, it is shown that they may be independent of the internal masses if and only if all the internal masses are equal or if the diagram is a loop. Their positions for the latter case are given. For singularities in the second class, it is shown that they are always independent of the internal masses and that they occur only for a very restricted set of diagrams. 作者及机构信息 张宗燧, 吴中发, 鞠长胜 1. 中国科学院 Authors and contacts T. S. CHANG, T. F. WU, T. C. JIU 1. 中国科学院 参考文献 [1] 施引文献