  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. The
resulting modified Hamiltonian contains the photon propagator directly. A
simple Fock-state variational trial function is used to derive relativistic
two-fermion equations variationally from the expectation value of the
Hamiltonian of the field theory. The interaction kernel of the equation is
shown to be, in essence, the invariant M-matrix in lowest order. Solutions of
the two-body equations are presented for muonium like system for small coupling
strengths. The results compare well with the observed muonium spectrum, as well
as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are
discussed.
