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 Lambda and recover the alpha(2)-term of the self-energy, where alpha 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 alpha. This implies that perturbation theory in alpha is correct if Lambda is fix. As an immediate consequence we obtain enhanced binding for electrons. (C) 2003 Elsevier Inc. All rights reserved.