09-48 Jean-Marie Barbaroux, Thomas Chen, Semjon Vugalter, Vitali Vougalter

Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED (495K, pdf, 47 pages) Mar 12, 09

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Abstract. We determine the exact expression for the hydrogen ground state 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 ground state 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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