  We consider a reformulation of QED in which covariant Green functions are
used to solve for the electromagnetic field in terms of the fermion fields. It
is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be
obtained in the canonical equal-time formalism for the case where there are no
free photons. These eigenstates lead to two- and three-body Dirac-like
equations with electromagnetic interactions. Perturbative and some numerical
solutions of the two-body equations are presented for positronium and
muonium-like systems, for various strengths of the coupling.

Nuclear Theory