The renormalized electron mass in non-relativistic quantum electrodynamics

Abstract

This work addresses the problem of infrared mass renormalization for a non-relativistic electron minimally coupled to the quantized electromagnetic field (the standard, translationally invariant system of an electron in non-relativistic QED). We assume that the interaction of the electron with the quantized electromagnetic field is subject to an ultraviolet regularization and an infrared regularization parametrized by σ > 0 . For the value p = 0 of the conserved total momentum of electron and photon field, bounds on the renormalized mass are established which are uniform in σ → 0 , and the existence of a ground state is proved. For | p | > 0 sufficiently small, bounds on the renormalized mass are derived for any fixed σ > 0 . A key ingredient of our proofs is the operator-theoretic renormalization group based on the isospectral smooth Feshbach map. It provides an explicit, finite algorithm for determining the renormalized electron mass at p = 0 to any given precision.