Global solvability of massless Dirac-Maxwell systems
  We consider the Cauchy problem of massless Dirac-Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be extended via analogous methods to Dirac-Higgs-Yang-Mills theories. 
Nicolas Ginoux, Olaf M\"uller
math.AP