Quantitative estimates on the Hydrogen ground state energy 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 $O({\alpha }^5\log {\alpha }^{-1})$, 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.

AMS Latex, 51 pages

References in corpus (2)

• Renormalized Electron Mass in Nonrelativistic QED
• Non-analyticity of the groud state energy of the Hamiltonian for Hydrogen atom in non-relativistic QED

Cited by in corpus (10)

• Ground States in the Spin Boson Model
• On enhanced binding and related effects in the non- and semi-relativistic Pauli-Fierz models
• On Asymptotic Expansions in Spin Boson Models
• Van der Waals-London interaction of atoms with pseudo-relativistic kinetic energy
• Ground States for translationally invariant Pauli-Fierz Models at zero Momentum
• Ground state properties in non-relativistic QED
• Scale Dependence of the Retarded van der Waals Potential
• Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED. II. The spin case
• Renormalization Analysis for Degenerate Ground States
• Smoothness and analyticity of perturbation expansions in QED