Annales Henri Poincaré

, Volume 11, Issue 8, pp 1487–1544

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


    • Centre de Physique Théorique
    • Département de MathématiquesUniversité du Sud Toulon-Var
  • Thomas Chen
    • Department of MathematicsUniversity of Texas at Austin
  • Vitali Vougalter
    • Department of Mathematics and Applied MathematicsUniversity of Cape Town
  • Semjon Vugalter
    • Mathematisches InstitutLudwig-Maximilians-Universität München

DOI: 10.1007/s00023-010-0064-1

Cite this article as:
Barbaroux, J., 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.

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