Renormalized Electron Mass in Nonrelativistic QED

TL;DR

This paper proves that in nonrelativistic QED, the energy of a dressed electron is smoothly dependent on momentum near zero, with a positive lower bound on its second derivative, using iterative analytic perturbation theory.

Contribution

It establishes the twice differentiability of the electron energy function and a positive lower bound on its second derivative in nonrelativistic QED for small coupling.

Findings

Energy function E_|P| is twice differentiable near P=0

Second derivative of E_|P| is bounded below by a positive constant

Results are obtained using iterative analytic perturbation theory

Abstract

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