Numerical Techniques for High-Precision Multi-Loop Calculations in Quantum Electrodynamics and Scalar Field Theories

多环计算在量子场论，特别是量子电动力学中，随着时间的推移变得越来越重要，因为许多高精度的实验和基本常数的确定依赖于可以从这些强大的理论工具中提取的预测。重整化微扰场论是最准确理解自然界系统和物理性质的基础。在本建议中，我们将重点介绍用于评估具有许多潜在应用的多环路图的一般数值技术，以及在各种特别感兴趣的情况下的具体计划计算。这些都与兰姆位移和束缚电子g因子的高阶结合修正，以及对氦超流动性等关键现象的微扰重整化群处理有关，最近的一个实验产生了一个比现有最佳理论更准确的值。

Multi-loop calculations in quantum field theory, especially quantum electrodynamics, have become more and more important along the years because many high-precision experiments and determinations of fundamental constants rely on predictions which can be extracted from these powerful theoretical tools. Renormalized perturbative field theory forms the basis for the most accurately understood systems and physical properties in nature. In this proposal, we focus on general numerical techniques for the evaluation of multi-loop diagrams, with numerous potential applications, and on specific planned calculations in various cases of particular interest. These are related to rather urgent aspects of higher-order binding corrections to the Lamb shift and to the bound-electron g-factor, and on the perturbative renormalization group treatment of critical phenomena like the superfluidity of helium, where a recent experiment has produced a value which is more accurate than the best available theory.