Note on the Infrared Catastrophe
Note on the Infrared Catastrophe
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关于红外线灾难的注释
DOI：
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发表时间：
1950
期刊：
影响因子：
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通讯作者：
T. Kinoshita
中科院分区：
文献类型：
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作者：
T. Kinoshita
对由固定力中心散射的电子的弹性散射进行校正。该过程由两部分组成： 1) 入射电子（动量 P .. ，JJ= 1, 2, 3,4）被散射中心散射成最终状态（q .. -k .. ），并伴随着光量子（k .. ）的发射。对这一过程的矩阵元素进行平方，可以获得 e2/n.c 阶的横截面。 2）在入射电子（P .. ）散射到最终电子（q .. ）期间，发射出一个虚拟量子并被该电子重新吸收，并且在最终状态下不存在。该过程给出了弹性散射矩阵元素的 e2/n.c 修改，并与后者相结合，对原始横截面进行了 e2/fic 校正。从 Smatrix 的幺正性中很容易看出，这些横截面的总和与对应于图 1 中的四个图的矩阵元素实部的集合成正比。每个图都涉及上述两个过程，因此，预计矩阵适当处理低频量子的发散，并且当考虑到对所考虑的横截面做出贡献的所有相关过程时，它总是消失1）。但目前还没有令人信服的解释为什么总是会发生这种红外灾难的抵消。在这篇文章中，我们想从Tomonaga-Schwinger理论的角度给出一些关于这种现象的机制的思考结果。作为最简单的例子，我们首先关注二阶辐射
correction to the elastic scattering of an electron scattered by a fixed center of force. This process consists of two parts: 1) An -incident electron (with momentum P .. , JJ= 1, 2, 3,4) is scattered by the scattering center into a final state (q .. -k .. ) accompanied by an emission of a light quantum (k .. ). Squaring the marix element for this process one obtains a cross section of the order e2/n.c. 2) During the incident electron (P .. ) is scattered into a final one (q .. ), a virtual quantum is emitted and reabsorbed by this electron and it does not exist in the final state. This process gives an e2/n.c modification of the matrix element for the elasiic scattering and is combined with the latter to give an e2/fic correction to the original cross section. As is easily seen from the unitarity of the Smatrix, the sum of these cross sections is proportional to the collection of real parts of the matrix elements corresponding to the four diagrams in Fig. 1. Each diagram involves both processes described above, and, therefore, it is expected that the divergences of matrix propriate treatment of low frequency quanta and it always disappears when one takes into accout all relating processes that give contributions to the cross section considered1). But there has been no convincing explanation why such cancellation of infrared catastrophe always occurs. In this note we want to give some results of considerations about the mechanism of this phenomenon from the view point of the Tomonaga-Schwinger theory. As the simplest example, we shall first be concerned with the second order radiative