RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

正电子是由电子和它的反粒子正电子组成的束缚系统。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可以忽略不计，所以利用束缚态量子电动力学（QED）的方法也可以从理论上计算出正电子的性质。因此，正电子是一种理想的系统，用于测试QED束缚态物理的极限，并用于探索在这种高精度水平上理论和实验之间的一致或不一致的后果。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富兰克林马歇尔学院的本科生将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、准备和发表描述其结果的演讲、以及以共同作者的身份在研究期刊上发表他们的工作，获得宝贵的经验。利用有效量子场理论非相对论QED （NRQED）对正电子能级进行高精度计算。NRQED适合于这项工作，因为典型的原子系统的能量和动量，如正电子，与电子的静止能量相比是很小的。散度将使用维度正则化处理。能级是电子-正电子到电子-正电子四点格林函数的极点的位置，它们的值将在NRQED中使用束缚态摄动理论计算。对于氢原子这样的原子来说，反冲修正很小，而在正电子中，反冲修正很大，这将成为这项工作的主要焦点。后坐力修正的计算将使用“部分积分”恒等式和最近在低阶近似下对正电子进行测试的相关方法进行。改进的实验结果和更高精度的理论将结合起来，使束缚态量子力学成为迄今为止最严格的测试之一。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Positronium is the bound system consisting of the electron and its antiparticle, the positron. As such, it forms an “exotic atom”, similar in many ways to 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. Consequently, positronium is an ideal system for testing the limits of QED bound state physics and for exploring the consequences of agreement or disagreement between theory and experiment at this high level of precision. The activities involved in calculating the positronium energy levels will be of great educational value to the undergraduate students at Franklin & Marshall College 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 preparing and giving presentations describing their results, and by publishing their work as co-authors in research journals. Positronium energy levels will be calculated to high precision using the effective quantum field theory Non-Relativistic QED (NRQED). NRQED is appropriate for this work because the energies and momenta typical of atomic systems such as positronium are small compared to the electron rest energy. Divergences will be dealt with using dimensional regularization. Energy levels can be found as the positions of the poles of the electron-positron to electron-positron four-point Green's function and their values will be calculated using bound-state perturbation theory in NRQED. Recoil corrections, which are small for atoms such as hydrogen, are large in positronium and will form a major focus of this work. Calculations of recoil corrections will be performed using the "integration by parts" identities and related methods that have recently been tested for positronium at a lower order of approximation. Improved experimental results and higher precision theory will combine to give bound-state QED one of its most stringent tests to date.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.