Effective dynamics of an electron coupled to an external potential in   non-relativistic QED
  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. 
Volker Bach, Thomas Chen, Jeremy Faupin, Juerg Froehlich, Israel   Michael Sigal
math-ph math.MP