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

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.