Non-analyticity of the groud state energy of the Hamiltonian for Hydrogen atom in non-relativistic QED

TL;DR

This paper calculates the ground state energy of a hydrogen atom model in non-relativistic QED up to fourth order in the fine structure constant, revealing its non-analytic behavior.

Contribution

It provides a detailed perturbative expansion of the ground state energy in non-relativistic QED and demonstrates the non-analyticity of the energy in the coupling constant.

Findings

Ground state energy computed up to fourth order in alpha

Non-analyticity of the ground state energy established

Implications for the stability analysis of quantum systems

Abstract

We derive the ground state energy up to the fourth order in the fine structure constant $\alpha$ for the translation invariant Pauli-Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we obtain the non-analyticity of the ground state energy of the Pauli-Fierz operator for a single particle in the Coulomb field of a nucleus.