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-matr ix theory, the restrictedness and incompleteness of the conventional renorm alization procedure has been overlooked in the literature. Therefore, in or der to achieve an unambiguous and complete renormalization of the U-evoluti on matrix, a new general renormalization concept, being valid in both nonre lativistic and relativistic QED, is developed. The application of the metho d leads, For the first time, to completely renormalized, general expression s for the U-matrix and the spectral line shape, including all orders of the atom-field interaction. Finally, as an illustrative example, explicit calc ulations are carried out in the case of the nonexponential, spontaneous Lym an alpha decay. (C) 2000 Elsevier Science B.V. All rights reserved.