Order and Chaos in Classical and Quantum Mechanics

量子电动力学（QED）是近年来研究的一个非常活跃的领域。S-矩阵理论和有效场论这两种理论方法可以系统地处理多电子系统，前者对高电荷态离子最有用，后者对中性的、少电子态原子最有用。由于理论的成功，该领域的另一个重要方向是利用实验和QED理论的高精度，使原子成为非QED物理的试验场。最引人注目的应用是重原子中的宇称不守恒（PNC），另一个重要的应用是核物理。本研究的第一个主要焦点将是氦的精细结构，作为确定精细结构常数的一种方法。极端复杂的电子g-2的方法，最近显示的错误发现木下？的计算，表明了另一种方法的价值。第二个重点将涉及对高电荷离子的研究，继续与K. T。劳伦斯利弗莫尔国家实验室。完成了类钠离子光谱的计算，并将计算范围沿着扩展到类铜离子.高电荷态离子的超精细分裂也将被研究。第三个研究领域是反冲修正。只有另一个研究小组研究过高度相对论系统中反冲的处理。G.阿德金斯和我一直在研究一种独立的方法来解决这个问题，并建议继续这项研究。反冲技术的另一个应用是光子-Z玻色子交换图的处理，它具有一个尚未在Bethe-Salpeter框架中评估的束缚奇点。最终目标是编写一本关于束缚态量子场论的教科书，具有更广泛的影响。上述研究中使用的大多数技术还没有以教科书的形式得到很好的描述，这样做，沿着对Bethe和Salpeter的专著进行急需的更新，是这项工作的目的。

Quantum Electrodynamics (QED) has been a very active field in recent years. Twotheoretical techniques, S-matrix theory and effective field theory, allow the systematictreatment of many-electron systems, with the former being most useful for highlycharged ions and the latter for neutral, few-electon atoms.Given the success of the theory, another important direction the field is going in is theuse of the high precision of both experiment and QED theory to make atoms testinggrounds for non-QED physics. The most striking use has been parity nonconservation(PNC) in heavy atoms, and another important use is in nuclear physics.A first major focus of this research will be in the fine structure of helium as a way ofdetermining the fine structure constant. The extreme complexity of the electron g-2approach, recently shown by an error found in Kinoshita?s calculations, indicates thevalue of an alternative approach. Independent checks of a recent calculation ofPachucki are proposed.A second focus will involve research on highly charged ions, continuing a long standingcollaboration with K.T. Cheng of Lawrence Livermore National Laboratory. Completionof calculations of the spectra of sodiumlike ions along with extension to copperlike ionsis proposed. Hyperfine splitting in highly charged ions will also be studied.A third research area is recoil corrections. The treatment of recoil in a highly relativisticsystem has been treated only by one other group. G. Adkins and I have been workingon an independent approach to the problem, and continuation of this research isproposed. Another use of recoil techniques is in the treatment of photon-Z bosonexchange diagrams, which have a binding singularity that has not yet been evaluated ina Bethe-Salpeter framework.A final goal, with broader impact, is writing a textbook on bound state quantum fieldtheory. Most of the techniques used in the research described above have not yet beenwell described in textbook form, and doing this, along with giving a much needed updateof Bethe and Salpeter's monograph, is the intention of this work.