Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED

Details Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED

2009-03-11

arxiv.org/abs/0903.1854v2

Ann. H. Poincare, 11 (8), 1487-1544, 2010

Physics

Mathematical Physics

AMS Latex, 51 pages

Scientific paper

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

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