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

量子电动力学和标量场论中高精度多环计算的数值技术

• 批准号: 28853827
• 负责人: Privatdozent Dr. Maarten DeKieviet, since 11/2009
• 金额: --
• 依托单位: AG Quantentheorie und Vielteilchensysteme
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/28853827?language=en
• 关键词: Numerical; Techniques; Precision; Multi; Loop

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.

量子场论中的多圈计算，特别是量子电动力学，沿着这些年来变得越来越重要，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。重整化微扰场论是自然界中最准确理解系统和物理性质的基础。在这个建议中，我们专注于一般的数值技术的多回路图的评估，具有许多潜在的应用，并在特定的计划计算在各种情况下，特别感兴趣。这些都与兰姆位移和束缚电子g因子的高阶束缚修正的相当紧迫的方面有关，以及对氦的超流性等临界现象的微扰重整化群处理，最近的实验产生了一个比现有最好的理论更准确的值。