Hyperfine splitting in non-relativistic QED: uniqueness of the dressed   hydrogen atom ground state
  We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-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. 
Laurent Amour and J\'er\'emy Faupin
math-ph math.MP math.SP