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