Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

doi:10.1088/1674-1056/20/2/020302

中国物理B ›› 2011, Vol. 20 ›› Issue (2): 20302-020302.doi: 10.1088/1674-1056/20/2/020302

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

徐建军¹, 倪光炯², 楼森岳³

(1)Department of Physics, Fudan University, Shanghai 200433, China; (2)Department of Physics, Fudan University, Shanghai 200433, China; Department of Physics, Portland State University, Portland, OR97207, USA; (3)Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China; Department of Physics, Ningbo University, Ningbo 315211, China

收稿日期:2010-03-11 修回日期:2010-10-08 出版日期:2011-02-15 发布日期:2011-02-15

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

Ni Guang-Jiong(倪光炯)^a)b)†, Xu Jian-Jun(徐建军)^a)‡, and Lou Sen-Yue(楼森岳)^c)d)

^a Department of Physics, Fudan University, Shanghai 200433, China; ^b Department of Physics, Portland State University, Portland, OR97207, USA; ^c Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China; ^d Department of Physics, Ningbo University, Ningbo 315211, China

Received:2010-03-11 Revised:2010-10-08 Online:2011-02-15 Published:2011-02-15

摘要/Abstract

摘要： Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S--2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space--time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state---a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.

关键词: reduced Dirac equation, Lamb shift, off-mass-shell

Abstract: Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S–2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space–time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state–a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.

Key words: reduced Dirac equation, Lamb shift, off-mass-shell

中图分类号: (Relativistic wave equations)

03.65.Pm

11.10.Gh (Renormalization) 12.20.Ds (Specific calculations)

倪光炯, 徐建军, 楼森岳. Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics[J]. 中国物理B, 2011, 20(2): 20302-020302.

Ni Guang-Jiong(倪光炯), Xu Jian-Jun(徐建军), and Lou Sen-Yue(楼森岳). Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics[J]. Chin. Phys. B, 2011, 20(2): 20302-020302.

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Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

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