Nonrelativistic calculation of the Lamb shift without applying the dipole approximation

Abstract

By applying a method which exploits the O(4) symmetry of the nonrelativistic hydrogen atom, the Lamb shift is calculated without making the dipole approximation. Similar calculations in the dipole approximation have been previously carried out by Lieber. The advantage of our calculations is that, without introducing a cutoff-frequency, analytical and numerical results for energy-level (Lamb) shifts, in which the self-energy of the free electron is completely separated, are obtained. Since the obtained results are finite, the significance of the retardation effects is clearly demonstrated. Furthermore, a comparison is also made with the results obtained by other authors.