Exact Results in Quantum Theory

The two-loop electron self-energy is one of the most problematic effects in the hydrogen Lamb shift, whose theory is the cornerstone for determination of the Rydberg constant [1]. Its contribution is presently obtained from combining the numerical all-order (in the nuclear binding field) calculations [2] and the calculations based on the expansion in the binding field [3,4]. The accuracy of the all-order calculations is limited by the convergence of the partial-wave expansion, whereas the accuracy of the expansion calculations is limited by the unknown higher-order contributions. Recently, methods with improved the partial-wave expansion convergence were developed for the one-loop self-energy problem [5,6]. I will discuss the recent developments in all-order two-loop calculations [7] and their consequences for the determination of the Rydberg constant. [1] E. Tiesinga, P. J. Mohr, D. B. Newell, and B. N. Taylor, Rev. Mod. Phys. 93, 025010 (2021). [2] V. A. Yerokhin, Phys. Rev. A 80, 040501(R) (2009). [3] K. Pachucki and U. D. Jentschura, Phys. Rev. Lett. 91, 113005 (2003). [4] S. G. Karshenboim, A. Ozawa, and V. G. Ivanov, Phys. Rev. A 100, 032515 (2019). [5] V. A. Yerokhin, K. Pachucki, and V. M. Shabaev, Phys. Rev. A 72, 042502 (2005). [6] J. Sapirstein, K. T. Cheng, Phys. Rev. A 108, 042804 (2023). [7] V. A. Yerokhin, Z. Harman, Ch. Keitel, submitted.