Positronium states in three-dimensional QED

The e--e⁺bound state spectrum of three-dimensional QED is investigated in the quenched ladder approximation to the homogeneous Bethe-Salpeter equation with fermion propagators from a rainbow approximation Schwinger-Dyson solution with a variable fermion mass. 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 are made with existing nonrelativistic calculations.