Positronium States in QED3

Abstract

The $e^{-}$-$e^{+}$ bound state spectrum of QED3 is investigated in the quenched ladder approximation to the homogeneous Bethe-Salpeter equation with fermion propagators from a rainbow approximation Schwinger-Dyson equation. A detailed analysis of the analytic structure of the fermion propagator is performed so as to test the appropriateness of the methods employed. The large fermion mass limit of the Bethe-Salpeter equation is also considered, including a derivation of the Schrödinger equation, and comparisons made with existing non-relativistic calculations.

22 pages plus 12 postscript figures, uuencoded