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

• Final Report Year: 2011

Final Report Abstract

Multi-loop calculations in quantum field theory, especially quantum electrodynamics, have become more and more important along the years because many highprecision 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 the project, our focus was on general numerical techniques for the evaluation of multi-loop diagrams, and on specific planned calculations in various cases of particular interest. In practice, and in accordance with the original proposal, we have been mainly concerned with some specific higherorder calculations for bound states, which address the main theoretical challenges in a project pursued together with experimentalists from the National Institute of Standards and Technology near Washington, DC (USA).

Publications

• "Fundamental constants and tests of theory in Rydberg states of hydrogen-like ions," Phys. Rev. Lett. 100, 160404 (2008)
  U. D. Jentschura, P. J. Mohr, J. N. Tan and B. J. Wundt
  
• "Relativistic (Zα)^2 Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States," Phys. Rev. A 80, 022505 (2009)
  B. J. Wundt and U. D. Jentschura