Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin

We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian H. There is no external potential and H fibers as ∫ H_pdp according to the total momentum p. We prove that the ground state subspace of H_p is two-fold degenerate provided the charge e and the total momentum p are sufficiently small. We also establish that the total angular momentum of the ground state subspace is ±1/2 and study the case of a confining external potential.