A novel complete treatment of the time-evolution of a spontaneously decaying atomic state in relativistic QED

A new method, which, for the first time to our knowledge, makes a complete treatment of a spontaneously decaying atomic state in relativistic QED possible, is presented. The method is based on a self-consistent projection-operator technique, developed recently by the author. A new physical real-transition interaction picture, in which the unobservable interaction of the free electron with the vacuum radiation field is eliminated, is introduced. This leads automatically to the familiar finite relativistic Lamb shift, without using the concept of the mass renormalization. Moreover, in this picture a new real-transition Hamiltonian is derived. Finally, by applying the method to the relativistic Lyman-σ spontaneous emission, explicit analytic results for the non-Markovian time evolution and the radiative line shape including the correct frequency (Lamb) shift are obtained