Theoretical and phenomenological studies concerning a possible new phase of QED

In this paper we present a variety of investigations inspired by the explanation of narrow $e^{+}$ $e^{\mathrm{-}}$ peaks in heavy-ion collisions as due to a possible new phase of QED. We extend, to the fourth order, previous calculations of the spectrum of QED in the strong-coupling phase. We formulate a program to study the properties of the electron propagator as a function of nonconstant background fields, using Monte Carlo techniques. We also construct a phenomenological model, based on the idea of a new phase, of some peculiar features of the heavy-ion scattering data. Motivated by the recent Bhabha-scattering experiments, we compute the effect on the Bhabha and annihilation cross sections of a narrow pseudoscalar state, including the contribution of the interference term.