### Abstract

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 α^{8}.

Original language | English |
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Pages (from-to) | 1927-1942 |

Number of pages | 16 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 8 |

DOIs | |

Publication status | Published - Mar 1 2002 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and General*,

*35*(8), 1927-1942. https://doi.org/10.1088/0305-4470/35/8/310