Annales Henri Poincaré

, Volume 11, Issue 8, pp 1487-1544

First online:

Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED

  • Jean-Marie BarbarouxAffiliated withCentre de Physique ThéoriqueDépartement de Mathématiques, Université du Sud Toulon-Var Email author 
  • , Thomas ChenAffiliated withDepartment of Mathematics, University of Texas at Austin
  • , Vitali VougalterAffiliated withDepartment of Mathematics and Applied Mathematics, University of Cape Town
  • , Semjon VugalterAffiliated withMathematisches Institut, Ludwig-Maximilians-Universität München


In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli–Fierz model up to the order α 5 log α −1, where α denotes the fine structure constant, and prove rigorous bounds on the remainder term of the order o(α 5 log α −1). As a consequence, we prove that the binding energy is not a real analytic function of α, and verify the existence of logarithmic corrections to the expansion of the ground state energy in powers of α, as conjectured in the recent literature.