Abstract :
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.
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