Theory of Light Hydrogenlike Bound States: High Order Corrections to Lamb Shift, Hyperfine Splitting, and g-Factors

近年来，类氢束缚态的高精度量子电动力学研究取得了稳步的进展。实验误差和理论精度都得到了显著改善。正如经常发生的那样，这种快速的进步导致了新的问题。在高精度量子电动力学束缚态理论领域中，长期存在的问题有：1.氢中1 S Lamb位移的理论误差应显著降低到1 kHz以下（2S Lamb位移的理论误差应显著降低到1 kHz以下）。μ素超精细分裂的理论误差应减小到10 Hz ~ 3左右。μ子氢的2S-2 P兰姆位移的理论误差应减小到0.001meV以下。轻类氢原子理论的所有主要理论问题都将在本研究中得到解决。其主要目标包括：1。完整计算了氢原子兰姆位移的所有三个环圈非反冲修正，其量级为\alpha ^3（Z\alpha）^5 m。这些是对兰姆转移最大的未知贡献。分别计算了氢和μ介子超精细分裂的三个环非反冲修正.完整计算了μ介子超精细分裂的所有三个环辐射反冲修正，其量级为\a^3（m/M）E_F。计算μ介子兰姆位移的\α ^2（Z \alpha）^4 m阶非对数修正.计算μ介子氢兰姆位移的\α ^2（Z \alpha）^3 m阶轻电子环贡献的光. 4.解决包含自旋为j \neq 1/2/1的粒子的系统中束缚态g因子理论的矛盾.

Recent years witnessed a steady progress in the field of high precision quantumelectrodynamics of hydrogenlike bound states. Both the experimental errors and theaccuracy of theory were signifcantly improved. As often happens this rapid progressleads to new problems. In the field of high precision quantum electrodynamic theory ofbound states the long term problems are as follows;1. The theoretical error of the 1S Lamb shift in hydrogen should be reduced signifcantlybelow the level of 1 kHz (and respectively of the 2S Lamb shift significantly below tenthof kHz)2. The theoretical error of the hyperfine splitting in muonium should be reduced to about10 Hz3. The theoretical error of the 2S-2P Lamb shift in muonic hydrogen should be reducedbelow .001meV.All main theoretical problems of the theory of light hydrogenlike atomes will beaddressed in the proposed research. Its main objectives include;1. Complete calculation of all three loop nonrecoil corrections of order \alpha^3(Z\alpha)^5m to the Lamb shift in hydrogen. These are the largest still unknowncontributions to the Lamb shift. Respective three loopnonrecoil corrections to hyperfine splitting in hydrogen and muonium also will becalculated.2. Complete calculation of all three loop radiative recoil corrections of order\alpha^3(m/M) E_F to hyperfine splitting in muonium.3. Calculation of nonlogarithmic corrections of order \alpha^2(Z \alpha)^4 m to the Lambshift in muonic.Calculation of light by light electron loop contribution of order \alpha^2(Z \alpha)^3 m tothe Lamb shift inmuonic hydrogen.4.Resolution of the discrepancy in the theory of bound state g factors in systemsincluding particles with spins j \neq 1/2/