Magnetic Monopoles and Charged States in Four-Dimensional, Abelian Lattice Gauge Theories

We construct physical states of arbitrary magnetic charge for the U (1) 4 lattice gauge theory and electrically charged states for the four-dimensional, noncompact Abelian Higgs model, or spinor QED, in the massless QED phase of these models. We discuss the infraparticle structure of monopoles and charged particles and show that, in the continuum limit (if it exists), the Lorentz group cannot be implemented unitarily on charged sectors.