On Radiation Reactions in Collision Processes. I

Directly after the striking confirmation of Lamb and Retherford(l) that the energy levels of the hydrogen atom deviate from the prediction obtained by Dirac's theory, Bethe(2) published a note on his theory that explained this experimental fact in terms of the reaction of the radiation field. This attempt draws our attention much, because it may indicate a possible path to overcome the fundamental difficulty of the quantum field theory, and that for the first time in close connection with reliable experimental data. The essential point of Bethe's theory lies in the following hypothesis: the self-energy of a free electron, i.e. thereadion of the field accompanied by the electron on itself when no external force is acting, is, though divergent in the present formalism of the theory, already included in the mass of the electron which we really observe; when, however, the electron is put in an external field, the finite deviation of the self-energy of this electron from that in thc standard state, which is of a free electron with the same kinetic energy as the average value of the bound one under con- sideration, is to be 'taken into account as causing e.g. the level-shift of the hydrogen atom in question.