Spectral Analysis of the Semi-relativistic Pauli-Fierz Hamiltonian
  We consider a charged particle, spin 1/2, 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 $H(P)$, $P\in \BbbR^3$. 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. 
Tadahiro Miyao, Herbert Spohn