Complete renormalization method beyond the conventional on-shell renormalization in both nonrelativistic and relativistic QED: renormalized expressions for the U-matrix and the spectral line shape

It is demonstrated that, because of its exclusive application in the S-matrix theory, the restrictedness and incompleteness of the conventional renormalization procedure has been overlooked in the literature. Therefore, in order to achieve an unambiguous and complete renormalization of the U-evolution matrix, a new general renormalization concept, being valid in both nonrelativistic and relativistic QED, is developed. The application of the method leads, for the first time, to completely renormalized, general expressions for the U-matrix and the spectral line shape, including all orders of the atom–field interaction. Finally, as an illustrative example, explicit calculations are carried out in the case of the nonexponential, spontaneous Lyman α decay.