Jentschura, Ulrich D.; Pachucki, Krzysztof Two-loop self-energy corrections to the fine structure. (English) Zbl 1017.81524 J. Phys. A, Math. Gen. 35, No. 8, 1927-1942 (2002). Summary: We investigate two-loop higher order binding corrections to the fine structure, which contribute to the spin-dependent part of the Lamb shift. Our calculation focuses on the so-called ‘two-loop self-energy’ involving two virtual closed photon loops. For bound states, this correction has proved to be notoriously difficult to evaluate. The calculation of the binding corrections to the bound-state two-loop self-energy is simplified by a separate treatment of hard and soft virtual photons. The two photon-energy scales are matched at the end of the calculation. We explain the significance of the mathematical methods employed in the calculation in a more general context, and present results for the fine-structure difference of the two-loop self-energy through the order of \(\alpha^8\). Cited in 1 Review MSC: 81V10 Electromagnetic interaction; quantum electrodynamics 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81T15 Perturbative methods of renormalization applied to problems in quantum field theory Keywords:spin-dependent part of the Lamb shift; virtual closed photon loops; two photon-energy scales Software:Mathematica PDFBibTeX XMLCite \textit{U. D. Jentschura} and \textit{K. Pachucki}, J. Phys. A, Math. Gen. 35, No. 8, 1927--1942 (2002; Zbl 1017.81524) Full Text: DOI arXiv