UC Davis

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, $$E_{\overrightarrow{P}}$$ , of a dressed electron is twice differentiable in the momentum $$\overrightarrow{P}$$ in a neighborhood of $$\overrightarrow{P}=0$$ . Furthermore, $$\frac{{\partial }^2{E}_{\overrightarrow{P}}}{(\partial |\overrightarrow{P}|{)}^2}$$ is bounded from below by a constant larger than zero. Our results are proven with the help of iterative analytic perturbation theory.