Self-energy of one electron in non-relativistic QED

We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed in Hainzl (Ann. H. Poincare´ , in press). We fix an arbitrary cutoff parameter L and recover the a2-term of the self-energy, where a is the coupling parameter representing the fine structure constant. Thereby we develop a method which allows to expand the self-energy up to any power of a: This implies that perturbation theory in a is correct if L is fix. As an immediate consequence we obtain enhanced binding for electrons. r 2003 Elsevier Inc. All rights reserved.