Spectral analysis of the semi-relativistic Pauli–Fierz hamiltonian

We consider a charged particle, spin , with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as H(P), P∈R3. We study the spectrum of H(P). In particular we prove that, for non-zero photon mass, the ground state is exactly two-fold degenerate and separated by a gap, uniformly in P, from the rest of the spectrum.