# 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.

## 4 Citations

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

- Mathematics
- 2010

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…

### Scale dependence of the retarded van der Waals potential

- Physics
- 2012

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit α → 0 together with the relative distance between the atoms increasing as α−γR,…

### On the ground state energy of the translation invariant Pauli-Fierz model. II.

- PhysicsDocumenta Mathematica
- 2012

In this note, we determine the ground state energy of the translation invariant Pauli-Fierz model to subleading order $O(\alpha^3)$ with respect to powers of the finestructure constant $\alpha$, and…

### Renormalization Group and Problem of Radiation

- Physics
- 2011

The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this…

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