QUANTUM ELECTRODYNAMICS AT SMALL DISTANCES
QUANTUM ELECTRODYNAMICS AT SMALL DISTANCES
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DOI：
10.1103/physrev.95.1300
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发表时间：
1954-01-01
期刊：
影响因子：
--
通讯作者：
LOW, FE
中科院分区：
文献类型：
--
作者：
GELLMANN, M;LOW, FE
在动量远大于电子质量的情况下，分别研究了光子和电子的重归一化传播函数D FC和S FC。我们发现，在这个区域内，耦合常数中所有阶的扰动级数的个别项都具有非常简单的渐近形式。把整个级数加起来的尝试只取得了部分成功。利用该理论的可重整性，发现该级数满足某些泛函方程。如果从级数中省略光子自能部分，使dfc = df，则sfc具有渐近形式A [p 2 m 2] n [i γ·p]−1，其中A= A (e 12), n= n （e 12）。当所有的图都包含在内时，会发现不太具体的结果。一个结论是，真空中测试电荷周围的电荷分布的形状在小距离上不依赖于耦合常数，除非通过比例因子。大动量传播函数的行为与理论中重整化常数的大小有关。由此证明了在微扰理论中作为具有发散系数的重整化耦合常数e1,2,4 π π π c的幂级数出现的未重整化耦合常数e1,2,4 π π π c，可以表现为两种方式之一：
The renormalized propagation functions D FC and S FC for photons and electrons, respectively, are investigated for momenta much greater than the mass of the electron. It is found that in this region the individual terms of the perturbation series to all orders in the coupling constant take on very simple asymptotic forms. An attempt to sum the entire series is only partially successful. It is found that the series satisfy certain functional equations by virtue of the renormalizability of the theory. If photon self-energy parts are omitted from the series, so that D FC= D F, then S FC has the asymptotic form A [p 2 m 2] n [i γ· p]− 1, where A= A (e 1 2) and n= n (e 1 2). When all diagrams are included, less specific results are found. One conclusion is that the shape of the charge distribution surrounding a test charge in the vacuum does not, at small distances, depend on the coupling constant except through a scale factor. The behavior of the propagation functions for large momenta is related to the magnitude of the renormalization constants in the theory. Thus it is shown that the unrenormalized coupling constant e 0 2 4 π ℏ c, which appears in perturbation theory as a power series in the renormalized coupling constant e 1 2 4 π ℏ c with divergent coefficients, may behave in either of two ways: