Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, E-(P) over right arrow, of a dressed electron is twice differentiable in the momentum (P) over right arrow in a neighborhood of (P) over right arrow = 0. Furthermore, partial derivative E-2((P) over right arrow)/partial derivative vertical bar(P) over right arrow vertical bar(2) is bounded from belowby a constant larger than zero. Our results are provenwith the help of iterative analytic perturbation theory.