Annales Henri Poincaré

, Volume 11, Issue 8, pp 1487–1544

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

  • Jean-Marie Barbaroux
  • Thomas Chen
  • Vitali Vougalter
  • Semjon Vugalter

DOI: 10.1007/s00023-010-0064-1

Cite this article as:
Barbaroux, JM., Chen, T., Vougalter, V. et al. Ann. Henri Poincaré (2010) 11: 1487. doi:10.1007/s00023-010-0064-1


In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli–Fierz model up to the order α5 log α−1, where α denotes the fine structure constant, and prove rigorous bounds on the remainder term of the order o(α5 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.

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Jean-Marie Barbaroux
    • 1
    • 2
  • 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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