Annales Henri Poincaré

, Volume 11, Issue 8, pp 1487–1544 | Cite as

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

  • Jean-Marie BarbarouxEmail author
  • Thomas Chen
  • Vitali Vougalter
  • Semjon Vugalter


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.


Binding Energy Photon Number Trial Function Total Momentum Infrared Singularity 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Jean-Marie Barbaroux
    • 1
    • 2
    Email author
  • Thomas Chen
    • 3
  • Vitali Vougalter
    • 4
  • Semjon Vugalter
    • 5
  1. 1.Centre de Physique ThéoriqueMarseille Cedex 9France
  2. 2.Département de MathématiquesUniversité du Sud Toulon-VarLa Garde CedexFrance
  3. 3.Department of MathematicsUniversity of Texas at AustinAustinUSA
  4. 4.Department of Mathematics and Applied MathematicsUniversity of Cape TownRondeboschSouth Africa
  5. 5.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMunichGermany

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