Bound-Electron g Factor and the Fine-Structure Constant
Dr. Ulrich Jentschura (MPI für Kernphysik, Heidelberg)

Recent progress in bound-state quantum electrodynamics has led to a significant increase in the accuracy of theoretical predictions of the bound-electron g factor. While the 2002 CODATA value of the fine-structure constant is mainly based on the measurement and theory of the free-electron g factor, the bound counterpart could serve as a source for an independent mesurement of the fine-structure constant of comparable precision, and thus, as an independent verification of one of most interesting fundamental constants of nature. The basis for the recent theoretical progress is discussed in detail, with an emphasis on dimensional regularization of Coulomb problems where Lorentz invariance is naturally broken. The three cutoff prescriptions for NRQED, (i) photon energy, (ii) photon mass, and (iii) dimensional regularization are contrasted and shown to lead to equivalent results for the g factor and one more fundamental prediction of QED, the Lamb shift in hydrogen and deuterium. The bound and free-electron g factor, and the Lamb shift, currently represent the most accurate theoretical predictions of field theory.