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

Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state