COULOMB GAUGE IN NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS AND THE SHAPE OF SPECTRAL LINES
COULOMB GAUGE IN NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS AND THE SHAPE OF SPECTRAL LINES
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DOI：
10.1098/rsta.1959.0008
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发表时间：
1959-01-01
影响因子：
--
通讯作者：
ZIENAU, S
中科院分区：
文献类型：
--
作者：
POWER, EA;ZIENAU, S
本文考察了库仑规范div A=0时非相对论量子电动力学的传输函数的格林并矢。假前兆的存在与传播子的某些动量空间表示中原点的奇异性有关，这允许给出消除这类前兆的处方。这一规定被证明等价于对与量子跃迁相关的近场的精确考虑。对衰变系统的状态向量进行了类比处理，并详细应用于自然谱线形状和受激辐射跃迁速率等问题。结果表明，在Lamb的实验背景下，Lamb 1057Mc/S谱线在氢气中的预期线形是洛伦兹的--强度反对塞曼分裂能量。这与阿诺斯和海特勒的预测相矛盾。另一方面，自然线条的分布油墨(圆形频率)有一个因数，即共振分母。给出了文献中相互冲突的转移率之间的明确位置。详细研究了计算与规范无关哈密顿量之间的关系。这种哈密顿量从传统的哈密顿量正则变换而来，被证明对内部的、动态的、量子化的电磁场是有效的；它在外加磁场的情况下的模拟是众所周知的。结果表明，这种变换消除了与虚假近场相关的许多困难，而且它还允许以一种简单的方式计算原子作为整体的某些辐射效应。
An examination is made of the Green dyadic for the propagation functions of non-relativistic quantum electrodynamics in the Coulomb gauge div A = 0. The existence of false precursors is shown to be associated with singularities at the origin in certain momentum space representations of the propagators and this allows a prescription to be given to eliminate such precursors. This prescription is proved equivalent to an exact consideration of the near fields associated with quantum transitions. The analogous treatment for the state vectors in decaying systems is carried through and is applied in detail to the problems of the shape of natural spectral lines and the transition rate for stimulated emission. It is shown that the expected line shape for the Lamb 1057 Mc/s line in hydrogen is Lorentzian within the context of Lamb’s experiments—intensity against Zeeman splitting energy. This is in contradiction to the predictions of Arnous and Heitler. The distribution ink(circular frequency) for a natural line, on the other hand, has a factorkatimes the resonant denominator. The definitive position between the conflicting transition rates in the literature is given. The relationship of the calculations to a gauge-independent Hamiltonian, considered in the paper, is investigated in detail. This Hamiltonian, transformed canonically from the conventional one, is shown to be valid for internal, dynamical, quantized electromagnetic fields; its analogue in the case of external applied fields being well known. It is demonstrated that the transformation eliminates many of the difficulties associated with the false near fields and that it also allows certain radiative effects, where the atom acts as a whole, to be computed in a straightforward manner.