# Hyperfine Splitting in Non-relativistic QED: Uniqueness of the Dressed Hydrogen Atom Ground State

@article{Amour2011HyperfineSI, title={Hyperfine Splitting in Non-relativistic QED: Uniqueness of the Dressed Hydrogen Atom Ground State}, author={Laurent Amour and J'er'emy Faupin}, journal={Communications in Mathematical Physics}, year={2011}, volume={319}, pages={425-450} }

We consider a free hydrogen atom composed of a spin-$${\frac{1}{2}}$$ nucleus and a spin-$${\frac{1}{2}}$$ electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.

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