论文标题
原子物理重新归一化的简介
An Introduction to Renormalization in Atomic Physics
论文作者
论文摘要
这些注释的目的是为原子物理学重新归一化的概念提供教学介绍。我们研究了非依赖性单电子原子的模型的量子动力学，该模型耦合到偶极子近似中的量子辐射场。电子和辐射场之间的相互作用是正规化的，使用合适的截止处方，从而消除了电子与高度紫外线（UV）场模式的耦合。随后，我们分析了相应的Heisenberg运动方程，并专注于在尖端电子的极限（即，当上述UV截止逐渐提升至无穷大时）的物理可观察力的行为（即，在极限）。我们确定作用在电子上的辐射反应力，并表明该力在逐渐去除紫外线截止时实际上朝着无穷大。这种分析最终导致电子质量的独特重新归一化处方，以及确定作用在电子上的亚伯拉罕·洛伦兹力。突出显示了仅仅素描的重归其化过程对空间维度的依赖性。最后，我们通过重新归一化的扰动理论提出了一个示例计算原子水平变化的示例，并还制定了重新归一化的平均场理论。
The purpose of these notes is to provide a pedagogical introduction to the concept of renormalization in atomic physics. We study quantum dynamics of a model of a nonrelativistic single electron atom coupled to the quantum radiation field in the dipole approximation. An interaction between the electron and the radiation field is regularized, using a suitable cutoff prescription which eliminates the coupling of the electron to the highly ultraviolet (UV) field modes. Subsequently, we analyze the corresponding Heisenberg picture equations of motion, and focus on behavior of physical observables in the limit of a pointlike electron (i.e., in the limit when the above mentioned UV cutoff is gradually lifted to infinity). We identify the radiation reaction force acting on the electron, and show that this force actually diverges towards infinity when gradually removing the UV cutoff. Such an analysis leads ultimately to an unique renormalization prescription for the electron mass, as well as to determination of the Abraham-Lorentz force acting on the electron. Dependence of the just sketched renormalization procedure upon the spatial dimension is highlighted. Finally, we present an example calculation of the atomic level shifts by means of the renormalized perturbation theory, and formulate also the renormalized mean field theory.
