, Volume 11, Issue 8, pp 1487-1544

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

Abstract

In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli–Fierz model up to the order α 5 log α −1, where α denotes the fine structure constant, and prove rigorous bounds on the remainder term of the order o(α 5 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.

Communicated by Volker Bach.