Gauge invariance in non–relativistic electrodynamics
Gauge invariance in non–relativistic electrodynamics
复制标题
非相对论电动力学中的规范不变性
DOI：
10.1098/rspa.2000.0587
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
R. Woolley
中科院分区：
文献类型：
--
作者：
R. Woolley
本文采用一种新的非相对论量子电动力学哈密顿格式，在该格式中，场势的规范任意性保持显式，研究了在允许共振效应和线展宽效应的情况下，各种版本的微扰理论的规范依赖性质。时变摄动理论被证明有严重的量规依赖问题，除非作出特别的修改。然后研究了s -矩阵理论的一个与时间无关的表述。远离共振，s矩阵在所有阶的微扰理论中都是规范不变的，这是由于非常精确地消去了规范相关项，这需要中间状态的完整集合；节能也起着至关重要的作用。然而，s矩阵在谐振（极）和非谐振背景中的明显分离导致了测量相关项的不完全抵消。将Heitler阻尼矩阵引入到t矩阵的积分方程中可以得到一个规范不变的结果。这为原子和分子与包括共振和阻尼效应的电磁辐射相互作用的规范不变s矩阵理论提供了基础。
A novel Hamiltonian scheme for non–relativistic quantum electrodynamics in which the gauge arbitrariness of the field potential is kept explicit is used to study the gauge–dependence properties of various versions of perturbation theory when resonance and line–broadening effects are admitted. Time–dependent perturbation theory is shown to have severe gauge–dependence problems unless ad hoc modifications are made. A time–independent formulation of S–matrix theory is then studied. Far from resonance, the S–matrix is gauge invariant in all orders of perturbation theory due to a very precise cancellation of gauge–dependent terms which requires, among other things, complete sets of intermediate states; energy conservation also has a crucial role. However, an obvious separation of the S–matrix into a resonant (pole) and non–resonant background leads to incomplete cancellation of the gauge–dependent terms. The introduction of the Heitler damping matrix into an integral equation for the T–matrix leads to a gauge–invariant result. This provides the basis for a gauge invariant S–matrix theory of atoms and molecules interacting with electromagnetic radiation that encompasses resonance and damping effects.