RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

正电子是电子和它的反粒子（正电子）的结合态。因此，它形成了一种“奇异原子”，在许多方面与传统的简单原子（如氢和氦）相似，但不同之处在于它独特的组成和它的湮灭倾向，它以高能光子的形式转化为纯电磁能量。正电子的许多特性，如能级和寿命，都可以通过高精度的实验得到。由于强相互作用和弱相互作用在该体系中可以忽略不计，因此利用束缚态量子电动力学（QED）方法也可以从理论上计算出正电子的性质。因此，正电子是测试电磁束缚态物理极限的理想系统。计算正电子能级所涉及的活动对于作为合作者参与这项工作的本科生具有很大的教育价值。学生将学习比通常在本科阶段遇到的更高级的理论方法和计算技术。他们将通过做研究，在专业会议上展示他们的成果，以及在研究期刊上作为共同作者发表他们的工作，获得宝贵的经验。低洼态（n=1和n=2）的正电子能级测量的不确定度约为1兆赫，目前正在进行实验，以显着降低其中一些不确定度。2S-1S转换特别有趣，因为它具有最小的自然线宽，因此具有最大的改进潜力。基态超细分裂之所以引起人们的兴趣，是因为最精确的实验结果与目前的理论并不一致。这些跃迁能量和更多的能量将被计算到一个新的精度水平。计算将基于低能量有效量子场论NRQED (Non-Relativistic QED)，它为研究非相对论性原子提供了一个自然而有效的框架。

Positronium is a bound state of an electron and its antiparticle, a positron. As such, it forms an "exotic atom," similar in many ways to the traditional simple atoms such as hydrogen and helium, but different because of its unique composition and because of its tendency to annihilate, transforming into pure electromagnetic energy in the form of high-energy photons. Many properties of positronium, such as energy levels and lifetimes, are accessible to high-precision experiments. Positronium properties can also be calculated theoretically to high precision using the methods of bound-state Quantum Electrodynamics (QED) because strong and weak interaction effects are negligible in this system. Consequently, positronium is an ideal system for testing the limits of electromagnetic bound state physics. The activities involved in calculating the positronium energy levels will be of great educational value to the undergraduate students involved as collaborators in this work. The students will learn theoretical methods and techniques of calculation more advanced than those usually encountered at the undergraduate level. They will gain valuable experience by doing the research, by presenting their results at professional meetings, and by publishing their work as co-authors in research journals.Positronium energy levels of low-lying states (n=1 and n=2) have been measured with uncertainties of roughly one MHz, and experiments are presently being developed to significantly reduce some of these uncertainties. The 2S-1S transition is of particular interest because it has the smallest natural linewidth and thus the greatest potential for improvement. The ground state hyperfine splitting is of interest because the most precise experimental results are not in accord with current theory. These transition energies and more will be calculated to a new level of precision. The calculations will be based on the low-energy effective quantum field theory NRQED (Non-Relativistic QED), which provides a natural and efficient framework for the study of non-relativistic atoms.