UC Davis

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