Quasipotential approach to the Bethe-Salpeter equation for positronium

Abstract

We discuss why the usual perturbation theory in unsuited for the study of bound states in quantum field theory. The Dyson equation for the 4-point Green's function is then presented and the Bethe-Salpeter equation derived from it, by using Green's function factorization around bound state poles. Some historical facts are given for context, after which we discuss a particular approach for solving the Bethe-Salpeter equation known as the quasipotential approach. We discuss several possible choices of gauge and two-body propagator that can be used within this scheme and use one to calculate the leading order hyperfine splitting in positronium.