Order and Chaos in Classical and Quantum Mechanics

经典与量子力学中的秩序与混沌

• 批准号: 0757752
• 负责人: John Delos
• 金额: $ 24万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0757752&HistoricalAwards=false
• 关键词: Order; Chaos; Classical; Quantum; Mechanics

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.

量子电动力学（QED）是近年来一个非常活跃的研究领域。两种理论技术，s矩阵理论和有效场论，允许系统地处理多电子系统，前者对高电荷离子最有用，后者对中性的、少电子的原子最有用。鉴于该理论的成功，该领域的另一个重要方向是利用实验和QED理论的高精度来使原子成为非QED物理的试验场。最引人注目的应用是在重原子中的宇称不守恒（PNC），另一个重要的应用是在核物理中。本研究的第一个重点将放在氦的精细结构上，作为确定精细结构常数的一种方法。电子g-2方法的极端复杂性，最近在木下？S的计算，表明另一种方法的价值。建议对pachucki最近的计算进行独立检查。第二个重点将涉及高电荷离子的研究，继续与劳伦斯利弗莫尔国家实验室的K.T. Cheng的长期合作。完成了类钠离子光谱的计算，并将其扩展到类铜离子。高电荷离子的超细分裂也将被研究。第三个研究领域是后坐力修正。在高度相对性系统中对后坐力的处理只有另一组研究过。G. Adkins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。反冲力技术的另一个用途是处理光子- z玻色子交换图，它有一个尚未在贝特-萨尔皮特框架中评估的结合奇点。一个最终目标，具有更广泛的影响，是编写一本关于束缚态量子场论的教科书。上面描述的研究中使用的大多数技术还没有在教科书中得到很好的描述，这样做，以及对Bethe和Salpeter的专著进行急需的更新，是这项工作的目的。