The Level Shift and the Anomalous Magnetic Moment of the Electron

The recent achievements both in experiment and theory have confirmed that the reaction of the radiation field is a really observable phenomenon and that one can calculate this effect in our present formalism of quantum theory if one employs some subtraction prescription. Thus Bethe(l) computed successfully the level shift of the hydrogen atom revealed by the experiment of Lamb and R etherford. (2) Following Bethe's idea, Tomonaga(S) has developed, independently of American authors, a so-called .. self-consistent" subtraction method which aims at disposing of the infinities in a self-consistent manner and obtaining finite results for various processes. In fact he and collaborators could show that the radiative corrections for the elastic scattering of the electron and the Compton scattering were made finite by this method.