Non-analyticity of the ground state energy of the hydrogen atom in non-relativistic QED

@article{Barbaroux2010NonanalyticityOT,
  title={Non-analyticity of the ground state energy of the hydrogen atom in non-relativistic QED},
  author={J. M. Barbaroux and Simeon A. Vugalter},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2010},
  volume={43},
  pages={474004}
}
We derive the ground state energy up to the fourth order in the fine-structure constant α 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. 

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