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

• Applicant: Privatdozent Dr. Maarten DeKieviet, since 11/2009
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2006 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 28853827

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.

• DFG Programme: Research Grants
• Ehemalige Antragsteller: Professor Dr. Dieter Bauer, from 12/2008 until 11/2009; Professor Dr. Ulrich Jentschura, until 12/2008