Effective dynamics of an electron coupled to an external potential in non-relativistic QED

TL;DR

This paper demonstrates that in non-relativistic QED, the electron's effective dynamics under an external potential can be accurately described by a Schrödinger equation with a kinetic term determined by the renormalized mass, accounting for radiative corrections.

Contribution

It establishes that the renormalized mass appears as the kinematic mass in the electron's response to external forces within non-relativistic QED, providing a rigorous derivation of effective dynamics.

Findings

Electron's response is governed by the renormalized mass.

Effective Schrödinger dynamics accurately describe long-time behavior.

Kinetic energy operator reflects the renormalized dispersion law.

Abstract

In the framework of non-relativistic QED, we show that the renormalized mass of the electron (after having taken into account radiative corrections) appears as the kinematic mass in its response to an external potential force. Specifically, we study the dynamics of an electron in a slowly varying external potential and with slowly varying initial conditions and prove that, for a long time, it is accurately described by an associated effective dynamics of a Schr\"odinger electron in the same external potential and for the same initial data, with a kinetic energy operator determined by the renormalized dispersion law of the translation-invariant QED model.