The Lorentz gauge in non-relativistic quantum electrodynamics
The Lorentz gauge in non-relativistic quantum electrodynamics
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非相对论量子电动力学中的洛伦兹规范
DOI：
10.1098/rspa.1982.0144
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
M. Babiker
中科院分区：
文献类型：
--
作者：
M. Babiker
它显示了非相对论性电动力学的传统拉格朗日如何导致洛伦兹规范中的一个理论，其中标量势与矢量势的横向和纵向分量被同等对待。这需要像Gupta-Bleuler方法一样引入不定度规。利用普通摄动理论对自由空间氢的兰姆位移进行计算，结果显示，标量场产生的部分贡献和纵向场的全部贡献在e2阶之间表现出显著的精确抵消，并且结果与贝特的表达式一致，其中只涉及横向光子。洛伦兹规范中的非相对论理论也被用来计算导体外带电粒子的阶-e2势，在那里同样表现出类似的精确消去。强调了洛伦兹规范中形式主义的优点，因为它提供了一个明确的程序来评估主要的库仑能量转移，特别是在粒子与活性介质表面的相互作用中，库仑规范可能存在问题。
It is shown how the conventional Lagrangian of non-relativistic electrodynamics leads to a theory in the Lorentz gauge where the scalar potential is treated on an equal footing with the transverse and longitudinal components of the vector potential. This requires the introduction of an indefinite metric as in the Gupta-Bleuler method. Calculations based on this approach with the use of ordinary perturbation theory for the free-space Lamb-shift of hydrogen are shown to exhibit remarkable exact cancellations between parts of the contribution arising from the scalar field and the entire contribution from the longitudinal field to order e2, and the result is in agreement with Bethe’s expression where only transverse photons are involved. The non-relativistic theory in the Lorentz gauge is also used to compute the order-e2 potential on a charged particle outside a conductor where again similar exact cancellations are exhibited. The advantage of the formalism in the Lorentz gauge is emphasized in that it provides an unambiguous procedure for the evaluation of the leading Coulomb energy shifts particularly in the interaction of particles with the surfaces of active media where the Coulomb gauge may be problematical.